Physics Book - User contributions [en]

Main Page

2015-12-03T04:13:55Z

J nwankwoh: /* 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]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
</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]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics 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]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrod Snell]]
*[[Johannes Kepler]]

</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]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Higgs Boson]]
*[[Inertia]]
</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]]
* [[Momentum at High Speeds]]
</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 the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear 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]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
*[[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 (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Path Independence of Electric Potential]]
</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]]
*[[Frame of Reference]]
*[[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]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
*[[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 Dipole Moment]]
**[[Magnetic Force]]
*[[Combining Electric and Magnetic Forces]]
**[[Magnetic Torque]]
**[[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]]
**[[Solenoid Applications]]
</div>
</div>

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

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[AC vs DC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
</div>
</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]]
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
**[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers from a physics standpoint]]
***[[Energy Density]]
**[[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]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
</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>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Waves]]
*[[Electromagnetic Spectrum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[The Microwave]]
</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]], [http://www.physicsbook.gatech.edu/VPython_basics beginner guide to VPython]

Main Page

2015-12-03T04:12:51Z

J nwankwoh: /* 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]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
</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]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics 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]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrod Snell]]
*[[Johannes Kepler]]

</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]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Higgs Boson]]
*[[Inertia]]
</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]]
* [[Momentum at High Speeds]]
</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 the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear 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]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
*[[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 (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Path Independence of Electric Potential]]
</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]]
*[[Frame of Reference]]
*[[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]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
*[[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 Dipole Moment]]
**[[Magnetic Force]]
*[[Combining Electric and Magnetic Forces]]
**[[Magnetic Torque]]
**[[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]]
**[[Solenoid Applications]]
</div>
</div>

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

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[AC vs DC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit while capacitor is charging]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
</div>
</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]]
**[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
**[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers from a physics standpoint]]
***[[Energy Density]]
**[[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]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
</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>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Waves]]
*[[Electromagnetic Spectrum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[The Microwave]]
</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]], [http://www.physicsbook.gatech.edu/VPython_basics beginner guide to VPython]

Current in a RC circuit

2015-12-03T04:11:42Z

J nwankwoh:

When a capacitor is connected in a circuit, it varies the current. This wiki will discuss the varying current in a circuit while the capacitor is '''''charging'''''.

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===
What is the current in the circuit 3 seconds after closing the switch?

'''SOLUTION'''

We know that <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math>, therefore;

<math>I = ({\frac{5}{2}})e^{\frac{-3}{2*1}} </math>

<math>I = ({\frac{5}{2}})e^{-1.5} </math>

<math>I = .557 A </math>

== See also ==
[[Steady State]]

[[Surface Charge Distributions]]

[[RC]]

Current in a RC circuit

2015-12-03T04:11:19Z

J nwankwoh:

When a capacitor is connected in a circuit, it varies the current. This wiki will discuss the varying current in a circuit while the capacitor is '''Charging'''.

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===
What is the current in the circuit 3 seconds after closing the switch?

'''SOLUTION'''

We know that <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math>, therefore;

<math>I = ({\frac{5}{2}})e^{\frac{-3}{2*1}} </math>

<math>I = ({\frac{5}{2}})e^{-1.5} </math>

<math>I = .557 A </math>

== See also ==
[[Steady State]]

[[Surface Charge Distributions]]

[[RC]]

Current in a RC circuit

2015-12-03T04:09:08Z

J nwankwoh: /* See also */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===
What is the current in the circuit 3 seconds after closing the switch?

'''SOLUTION'''

We know that <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math>, therefore;

<math>I = ({\frac{5}{2}})e^{\frac{-3}{2*1}} </math>

<math>I = ({\frac{5}{2}})e^{-1.5} </math>

<math>I = .557 A </math>

== See also ==
[[Steady State]]

[[Surface Charge Distributions]]

[[RC]]

Current in a RC circuit

2015-12-03T04:08:32Z

J nwankwoh: /* See also */

Current in a RC circuit

2015-12-03T04:07:55Z

J nwankwoh: /* Difficult */

Current in a RC circuit

2015-12-03T04:07:40Z

J nwankwoh: /* See also */

Current in a RC circuit

2015-12-03T04:07:26Z

J nwankwoh: /* See also */

Current in a RC circuit

2015-12-03T04:07:07Z

J nwankwoh: /* See also */

Current in a RC circuit

2015-12-03T04:05:29Z

J nwankwoh:

Current in a RC circuit

2015-12-02T18:43:24Z

J nwankwoh:

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===
What is the current in the circuit 3 seconds after closing the switch?

'''SOLUTION'''

We know that <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math>, therefore;

<math>I = ({\frac{5}{2}})e^{\frac{-3}{2*1}} </math>

<math>I = ({\frac{5}{2}})e^{-1.5} </math>

<math>I = .557 A </math>

==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?]]

Current in a RC circuit

2015-12-02T18:42:47Z

J nwankwoh: /* Connectedness */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===
What is the current in the circuit 3 seconds after closing the switch?

'''SOLUTION'''

We know that <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math>, therefore;

<math>I = ({\frac{5}{2}})e^{\frac{-3}{2*1}} </math>

<math>I = ({\frac{5}{2}})e^{-1.5} </math>

<math>I = .557 A </math>

==Connectedness==
Almost every appliance in use today utilized capacitors.

==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?]]

Current in a RC circuit

2015-12-02T18:29:09Z

J nwankwoh: /* Examples */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===
What is the current in the circuit 3 seconds after closing the switch?

'''SOLUTION'''

We know that <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math>, therefore;

<math>I = ({\frac{5}{2}})e^{\frac{-3}{2*1}} </math>

<math>I = ({\frac{5}{2}})e^{-1.5} </math>

<math>I = .557 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?]]

Current in a RC circuit

2015-12-02T18:24:41Z

J nwankwoh: /* Difficult */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===
What is the current in the circuit 3 seconds after closing the switch?

'''SOLUTION'''

We know that

==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?]]

Current in a RC circuit

2015-12-02T18:16:24Z

J nwankwoh: /* Middling */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> \mu = \mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T18:15:55Z

J nwankwoh: /* Middling */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''

<math> /mu = /mu_{0} </math>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T18:15:17Z

J nwankwoh: /* Middling */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the connecting wires in the circuit have electron mobility <math> \mu = .00006 </math>. </br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>? </br>

'''Solution'''</br>

<math> /mu = /mu_{0} </math> </br>

The inclusion of a capacitor in a circuit does cause current to vary with time but not by affecting the properties of the connecting wires. The capacitor changes the current by providing a growing electric field that opposes the original electric field.

===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T18:11:19Z

J nwankwoh: /* Middling */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
Originally, the circuit has electron mobility <math> \mu = .00006 </math>. <\br>

What is the new electron mobility, <math> \mu_{0} </math> , when <math> t = 3 </math>?

===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T18:00:12Z

J nwankwoh: /* Examples */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]
===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T17:59:54Z

J nwankwoh: /* Simple */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

What is the current in the circuit immediately after the switch is closed?

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T17:59:10Z

J nwankwoh: /* Simple */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

What is the current in the following circuit immediately after the switch is closed?

<math>V_s</math> = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T17:57:51Z

J nwankwoh: /* Simple */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

What is the current in the following circuit immediately after the switch is closed?

V_s = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_{net} = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T17:57:25Z

J nwankwoh: /* Simple */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

What is the current in the following circuit immediately after the switch is closed?

V_s = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_net = 0 </math>. <br/> <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
===Difficult===

==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?]]

Current in a RC circuit

2015-12-02T17:56:46Z

J nwankwoh: /* Simple */

Short Description of Topic

==The Main Idea==

Now that we have an understanding of steady state current, we can begin to examine the current in a RC circuit.

The current in a RC circuit differs from the current in a simple circuit because the capacitor acquires and releases charge; this varies the current.

[[File:CapacitorCurrent.GIF]]

This a graphical representation of the changing current and voltage on a capacitor with respect to time.
===A Mathematical Model===

The graph presented in the previous section is representative of a exponential equation. The current across a capacitor falls of like <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> where '''V''' is the voltage driving the current, '''R''' is the resistance of the circuit, '''t''' is time, and '''C''' is the capacitance of the capacitor.

As can be seen, as t approaches infinity, I approaches 0. In plain english, if the circuit is closed for a "very long time" the current in the circuit will approach zero.

===A Computational Model===

To aid in visualization, I will provide a "way of thinking".

When the switch is closed, the circuit is complete and the current begins to run. Remember current is just mobile electrons. The excess of electrons on one plate (along with the the consequential deficit of electrons on the other plate) provide a surface charge that repels the incoming electrons. Decreasing the flow of electrons decreases the current at the rate provided in the previous section.

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

What is the current in the following circuit immediately after the switch is closed?

V_s = 5 V<br/>
R = 2 Ohms<br/>
C = 1 Farad<br/>

[[File:RCcircuit.gif]]

'''SOLUTION'''

We can solve this problem mathematically or analytically.

Mathematically:

Looking at the equation for current in an RC circuit, <math>I = ({\frac{V}{R}})e^{\frac{-t}{RC}} </math> , and with the knowledge that <math> t \approx 0 </math>, we can see that the term <math> e^{\frac{-t}{RC}} \approx 1 </math> . Therefore, the current in the circuit is the same as it would be as if the capacitor wasn't there. <math> I = {\frac{V}{R}} </math> . <br/>

Analytically:

Think about it. What is it about an RC circuit that causes the current to decrease with time? It's simply the buildup of surface charge on the plate of the capacitor. This creates an electric field that opposes the electric field thats driving the original current. This buildup will go on until the opposing electric fields are equal and <math> E_net = 0 </math>. <br/> We will consider the current ''immediately'' after we close the switch. Electrons move quickly, but not instantaneously. Because of this, ''immediately'' after the switch is closed, surface charge hasn't had the time to buildup. So the electrons are only being driven by the original electric field. So we can see that <math> I = {\frac{V}{R}} </math>

===Middling===
===Difficult===

==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?]]

Current in a RC circuit

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J nwankwoh: /* Simple */

Current in a RC circuit

2015-12-02T17:47:38Z

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J nwankwoh: /* Simple */

Current in a RC circuit

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J nwankwoh: /* Simple */

Current in a RC circuit

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J nwankwoh: /* Simple */

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J nwankwoh: /* Simple */

File:RCcircuit.gif

2015-12-02T08:16:10Z

J nwankwoh: J nwankwoh uploaded a new version of "File:RCcircuit.gif"

File:RCcircuit.gif

2015-12-02T08:15:20Z

J nwankwoh:

Current in a RC circuit

2015-12-02T08:14:56Z

J nwankwoh: /* Simple */

Current in a RC circuit

2015-12-02T07:57:59Z

J nwankwoh: /* A Computational Model */

Current in a RC circuit

2015-12-02T06:45:48Z