Physics Book - User contributions [en]

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2015-12-01T17:50:07Z

Kjones313: /* Simple Circuits */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#Copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Quantum Theory]]
*[[Big Bang Theory]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Conductivity]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in a Solid]]
* [[Iterative Prediction of Spring-Mass System]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a ring]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting a Change in Rotation]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power]]
*[[Energy Graphs]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Relativistic Kinetic Energy]]
*[[Bohr Model]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Rutherford Experiment and Atomic Collisions]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
*[[Electric Force]]
*[[Polarization]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Motors and Generators]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electrical Resistance]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[RC]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers]]
*[[Resistors and Conductivity]]
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[Ampere's Law]]
**[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
</div>
</div>
*[[blahb]]
</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* An overview of [[VPython]]

Resistors and Conductivity

2015-12-01T00:02:37Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation

<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>

where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:

<math>R = {\frac{L}{σA}}</math>

where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words,

<math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math>

for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area,

<math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math>

for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words,

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math>

for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length,

<math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math>

for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,

<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>

<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>

<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.

<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result,

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>

<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>

<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:

<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-12-01T00:02:07Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation

<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>

where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:

<math>R = {\frac{L}{σA}}</math>

where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words,

<math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math>

for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area,

<math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math>

for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words,

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math>

for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length,

<math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math>

for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,

<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.

<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result,

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:

<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-12-01T00:01:06Z

Kjones313: /* Resistors in Series */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation

<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>

where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:

<math>R = {\frac{L}{σA}}</math>

where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words,

<math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math>

for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area,

<math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math>

for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words,

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math>

for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length,

<math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math>

for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-12-01T00:00:45Z

Kjones313: /* Resistors in Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation

<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>

where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:

<math>R = {\frac{L}{σA}}</math>

where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words,

<math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math>

for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area,

<math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math>

for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words,

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math>

for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length,

<math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math>

for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-12-01T00:00:25Z

Kjones313: /* Resistors in Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation

<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>

where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:

<math>R = {\frac{L}{σA}}</math>

where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words,

<math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math>

for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area,

<math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math>

for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words,

<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math>

for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length,

<math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math>

for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-30T23:59:41Z

Kjones313: /* Resistors in Series */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation

<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>

where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:

<math>R = {\frac{L}{σA}}</math>

where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words,

<math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math>

for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area,

<math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math>

for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-30T23:58:00Z

Kjones313: /* Relevant Equations */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation

<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>

where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:

<math>R = {\frac{L}{σA}}</math>

where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-30T23:57:33Z

Kjones313: /* Relevant Equations */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation

<math>R = {\frac{ΔV}{I}}</math>

where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation
<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>
where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:
<math>R = {\frac{L}{σA}}</math>
where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-30T23:57:13Z

Kjones313: /* Relevant Equations */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation
<math>R = {\frac{ΔV}{I}}</math>
where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation
<math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math>
where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself:
<math>R = {\frac{L}{σA}}</math>
where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T02:15:01Z

Kjones313: /* References */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T02:14:48Z

Kjones313: /* References */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

Created by Kevin Jones, 26 November 2015

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T02:11:54Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]

==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T02:03:31Z

Kjones313: /* References */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

#http://components.about.com/od/Components/a/Resistor-Applications.htm
#http://www.qrg.northwestern.edu/projects/vss/docs/thermal/3-whats-a-resistor.html
#http://www.resistorguide.com/books/
#http://www.electronics-tutorials.ws/resistor/res50.gif?81223b
#http://www.ceb.cam.ac.uk/data/images/groups/CREST/Teaching/impedence/series2.gif
#https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Resistor_symbol_America.svg/2000px-Resistor_symbol_America.svg.png

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:58:36Z

Kjones313: /* Further reading */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
==Further Reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:58:26Z

Kjones313: /* Further reading */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
==Further reading==

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:53:29Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
===Further reading===

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:52:15Z

Kjones313: /* Further reading */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
===Further reading===

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]
*[http://www.amazon.com/The-Resistor-Handbook-Cletus-Kaiser/dp/0962852554 The Resistor Handbook]

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:50:54Z

Kjones313: /* Further reading */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
===Further reading===

*[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
*[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:50:39Z

Kjones313: /* Further reading */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
===Further reading===

[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]
[http://www.barnesandnoble.com/w/resistor-theory-and-technology-felix-zandman/1101658170?ean=9781891121128 Resistor Theory and Technology, Ed. 1]

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:48:53Z

Kjones313: /* Further reading */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
===Further reading===

[http://www.resistorguide.com/e-book/ The Resistor Guide E-book]

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:35:43Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
*[[Georg Ohm]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:30:36Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Current]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:29:39Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:29:20Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:28:54Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:25:21Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

*[[Components]]
*[[Steady State]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:24:58Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

[[Components]]

[[Steady State]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:24:39Z

Kjones313: /* See also */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

[[Components]]
[[Steady State]]

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:11:04Z

Kjones313:

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:10:33Z

Kjones313:

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:SimpleCircuits]]

Resistors and Conductivity

2015-11-27T01:06:52Z

Kjones313:

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category: Simple Circuits]]

Resistors and Conductivity

2015-11-27T01:02:04Z

Kjones313:

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-27T00:53:47Z

Kjones313: /* Applications */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

===Heaters===

Another instance of the use of resistors in real life is heating. Heat is produced by the interaction of electrons as they flow through the resistor, essentially generating heat via friction.

===Other Examples===

Other applications of resistance include polygraph machines, radios, televisions, circuit boards, USB drives, and toasters. Any electronic with a circuit board, such as a cell phone or laptop, most likely utilizes a resistor of some type.

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-27T00:07:41Z

Kjones313: /* Connectedness */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Applications==

===Light Bulbs===

One of the most common applications of the concept of resistance is the incandescent light bulb. In such a light bulb, electricity is forced through a region of tungsten, which acts as a resistor. The energy in the particles is emitted as heat and light.

#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:41:39Z

Kjones313: /* In Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

The total current IT can also be found by summing the currents I1, I2, I3, and I4 running through each branch. The values of these currents can be obtained using the given voltage and the individual resistances within each branch.

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:38:04Z

Kjones313: /* In Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:
<math>I_T = {\frac{ΔV}{R_{equivalent}}} = {\frac{24 \ V}{4.8 \ Ω}} = 5 \ A</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:34:35Z

Kjones313: /* In Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

The voltage is again provided, and so it is possible to determine the total current IT using ΔV and Requivalent:

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:32:44Z

Kjones313: /* In Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>
<math>R_{equivalent} = 4.8 \ Ω</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:30:28Z

Kjones313: /* In Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120}} \ Ω</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:29:41Z

Kjones313: /* In Parallel */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{25}{120 \ Ω}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:28:31Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>
<math>{\frac{1}{R_{equivalent}}} = {\frac{1}{10 \ Ω}} + {\frac{1}{20 \ Ω}} + {\frac{1}{30 \ Ω}} + {\frac{1}{40 \ Ω}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:27:12Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + {\frac{1}{R_4}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:26:28Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel.
As a result, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:25:57Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel. As such, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:25:37Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel. As such, <math>>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T23:23:28Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]] Because the circuit at right has several possible paths of current, the resistors can be considered in parallel. As such, <math></math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Resistors and Conductivity

2015-11-26T22:08:21Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>

===In Parallel===

[[File:Resistors_in_Parallel_Example.gif|350 px|right]]

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Resistors in Parallel Example.gif

2015-11-26T22:06:50Z

Kjones313:

Resistors and Conductivity

2015-11-26T21:59:06Z

Kjones313: /* Examples */

A resistor is a component of a circuit that acts to reduce both the flow of current and the voltage levels within the circuit. When current runs through a resistor, the energy stored within particles is converted to another form of energy, typically indicated by the emission of light or heat. Conductivity is a property of a given material that refers to the material's ability to transmit electricity. Conductivity and resistivity are opposites; that is, the higher the conductivity of a material, the less resistance it offers to the flow of current.

==Relevant Equations==

The resistance of a material can be calculated in several ways. The most common method relates resistance to the potential difference and the conventional current of the circuit, using the equation <math>R = {\frac{ΔV}{I}}</math> where ΔV is the potential difference across the resistor and I is the conventional current running through the circuit.

The conductivity of a material can be found using the equation <math>σ = |q|nu = {\frac{\vec{J}}{\vec{E}}}</math> where |''q''| is the absolute value of the charge on each carrier, ''n'' is the number of charge carriers per m3, and ''u'' is the mobility of the charge carriers, '''J''' is the current density (I/A) in A/m2, and '''E''' is the electric field due to charges outside the material.

Another equation used to quantify resistance relates it to certain properties of the material and geometric properties of the resistor itself: <math>R = {\frac{L}{σA}}</math> where L is the length of the resistor, σ is the conductivity of the material, and A is the cross-sectional area of the resistor. This equation clearly demonstrates that resistivity and conductivity are inverses, as the conductivity constant can be found in the denominator.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Ohmic vs. Non-Ohmic Resistors==

Based on the equations above, it is clear that both conductivity and resistance are dependent on the mobility of the charge carriers, and so these values may vary as the current through an object changes. When the conductivity of a material is nearly constant, independent of the amount of current flowing through the resistor, we consider the material and resistor "ohmic." No matter is truly ohmic, as conductivity depends to some extent on temperature, and higher currents often lead to higher temperatures. Materials are generally considered ohmic, however, if the temperature change is minimal.

==Symbol and Units==

The conventional symbol for a resistor used in electrical circuit diagrams is shown below.

[[File:Resistor_Symbol.png|150px]]

The unit of resistance is the ohm (Ω), and the unit for conductivity is the Siemen per meter (S/m).

==Resistors in Series==

When ohmic resistors are connected along a single path with no branches, as in the figure below, they are said to be in series.

[[File:Resistors_in_Series.png|300px|center]]

Resistors in series are, in practice, equivalent to a single resistor with the combined resistance of its constituent resistors. In other words, <math>R_{equivalent} = R_1 + R_2 + R_3 + ... + R_n</math> for ''n'' resistors in series.

Because R = L/(σA), if every resistor is composed of the same material and has the same cross-sectional area, <math>L_{equivalent} = L_1 + L_2 + L_3 + ... + L_n</math> for ''n'' resistors in series.

==Resistors in Parallel==

When ohmic resistors are not connected in series, they can be connected in parallel (as in the figure below), creating several branches within a circuit.

[[File:Resistors_in_Parallel.png|300px|center]]

Several resistors in parallel are, in practice, equivalent to a single resistor with a resistance that is the reciprocal of the sum of reciprocals of the individual resistances. In other words, <math>{\frac{1}{R_{equivalent}}} = {\frac{1}{R_1}} + {\frac{1}{R_2}} + {\frac{1}{R_3}} + ... + {\frac{1}{R_n}}</math> for ''n'' resistors in parallel.

Because 1/R = (σA)/L, if every resistor is composed of the same material and has the same length, <math>A_{equivalent} = A_1 + A_2 + A_3 + ... + A_n</math> for ''n'' resistors in parallel.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===In Series===

[[File:Resistors_in_Series_Example.gif|350px|left]] Because the circuit at left has no branches, the resistors can be considered in series. As such, the values of the resistance of the individual resistors can be summed to find the equivalent resistance. Thus,
<math>R_{equivalent} = R_1 + R_2 + R_3 + R_4</math>
<math>R_{equivalent} = 65 \ Ω + 84 \ Ω + 73 \ Ω + 10 \ Ω</math>
<math>R_{equivalent} = 232 \ Ω</math>

Using this equivalent resistance and the given voltage (25 V), it is possible to find the value of the current running through the circuit after passing through the resistors.
<math>I = {\frac{ΔV}{R_{equivalent}}} = {\frac{25 \ V}{232 \ Ω}} \approx 0.108 \ A</math>
===In Parallel===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]