Physics Book - User contributions [en]

R Circuit

2017-11-27T18:50:13Z

MattMunns: /* Example Problems */

Claimed by Matthew Munns - Fall 2017

Resistors may exist in a circuit and resist electric charge. The resistance of a resistor depends on the properties of the material and the area of the resistor. These two attributes will be investigated later in the page.

Resistors may be ohmic or non-ohmic. An ohmic resistor has a conductivity that is nearly constant, while a non-ohmic resistor will vary depending on the conditions. This page will focus on ohmic resistors in a complex circuit.

The following is an image of an ohmic resistor like the resistor used in lab:
[[File:ResistorResize.jpg]]
==History==
Georg Simon Ohm, born in 1789, discovered Ohm's law. This law relates the current, voltage, and resistance across a resistor. His law was widely accepted by 1850. Ohm's law became the fundamental law in circuit analysis. In 1959, inventor Otis Boykin filed a patent for a resistor that allows manufacturers to designate a value of resistance for a piece of wire in equipment. In 1962, he patented an improved version, which could withstand more extreme conditions. This reduced the cost and increased the reliability of a variety of electronic products. <ref>{{cite web|work=The Philadelphia Tribune|title=Otis Boykin: Invented an Improved Electrical Resistor| publisher=The Philadelphia Tribune|url=http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html}}</ref>

==Mathematics==

As discussed above, resistance of a material is dependent on two factors: the properties of the material, and the area of the resistor.

From the above factors, we get the following definition of resistance:
<math>R = \frac{L}{σ A}</math>

In this definition <math> L </math> is the length of the resistor, <math> A </math> is the cross-sectional area of the resistor, and <math> σ </math> is the conductivity of the material.
<math> σ </math> can be further broken down to show <math> σ = |q|nu </math>.

==In A Circuit==

There is a change in potential energy across a resistor, which is useful when evaluating the loop rule in a circuit with resistors. The change in potential across a resistor is <math> I = \frac{ΔV}{R} </math>
Knowing this equation allows one to solve for <math> ΔV </math> if given <math>I</math> and either <math>R</math> or the components of <math>R</math> enumerated above.

In the case of a circuit resistors, the loop rule might look something like:
<math> |emf| = I_{1}R_{1} + I_{2}R_{2}</math>

==Equations Derived==
From the definition of resistance and the voltage potential formula discussed above, a number of useful equations can be derived and solved.
The first equation is <math> v = uE</math> where <math> E </math> is electron field , <math> u</math> as electron mobility, and <math> v</math> is drift speed.

This equation offers insight into the microscopic view of the resistor.

The second equation that can be derived is <math> I = |q|nAv</math>.
This equation can be used, in addition to the above equation <math> I = \frac{ΔV}{R}</math> to solve for macroscopic properties of the resistor.

==Example Problems==
===Easy Example===

'''Question:'''
Use the loop rule to calculate the voltage drop across each resistor. Then ensure that your answer is correct.
[[File:EasyExample.JPG]]

'''Answer:'''

[[File:EasyExampleAnswerResize.jpg]]

===Difficult Example===
https://www.youtube.com/watch?v=BW7U_5BtH-8

==Applications==

'''1.How is this topic connected to something that you are interested in?''' I am very interested in computers and I know that circuitry is the foundation of computers and other electronic equipment.

'''2.How is it connected to your major?''' My major is Industrial Engineering, and although I won't study resistors directly in any of my classes, I understand that resistors are crucial in the creation of the tools all engineers and scientists use such as computers and calculators.

'''3.Is there an interesting industrial application?''' As stated above, resistors are widely used in electric circuits. They are used to reduce current flow, change signal levels, and terminate transmission.

==Bibliography==
<references> http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html <references/>

R Circuit

2017-11-24T22:00:57Z

MattMunns: /* Easy Example */

Claimed by Matthew Munns - Fall 2017

Resistors may exist in a circuit and resist electric charge. The resistance of a resistor depends on the properties of the material and the area of the resistor. These two attributes will be investigated later in the page.

Resistors may be ohmic or non-ohmic. An ohmic resistor has a conductivity that is nearly constant, while a non-ohmic resistor will vary depending on the conditions. This page will focus on ohmic resistors in a complex circuit.

The following is an image of an ohmic resistor like the resistor used in lab:
[[File:ResistorResize.jpg]]
==History==
Georg Simon Ohm, born in 1789, discovered Ohm's law. This law relates the current, voltage, and resistance across a resistor. His law was widely accepted by 1850. Ohm's law became the fundamental law in circuit analysis. In 1959, inventor Otis Boykin filed a patent for a resistor that allows manufacturers to designate a value of resistance for a piece of wire in equipment. In 1962, he patented an improved version, which could withstand more extreme conditions. This reduced the cost and increased the reliability of a variety of electronic products. <ref>{{cite web|work=The Philadelphia Tribune|title=Otis Boykin: Invented an Improved Electrical Resistor| publisher=The Philadelphia Tribune|url=http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html}}</ref>

==Mathematics==

As discussed above, resistance of a material is dependent on two factors: the properties of the material, and the area of the resistor.

From the above factors, we get the following definition of resistance:
<math>R = \frac{L}{σ A}</math>

In this definition <math> L </math> is the length of the resistor, <math> A </math> is the cross-sectional area of the resistor, and <math> σ </math> is the conductivity of the material.
<math> σ </math> can be further broken down to show <math> σ = |q|nu </math>.

==In A Circuit==

There is a change in potential energy across a resistor, which is useful when evaluating the loop rule in a circuit with resistors. The change in potential across a resistor is <math> I = \frac{ΔV}{R} </math>
Knowing this equation allows one to solve for <math> ΔV </math> if given <math>I</math> and either <math>R</math> or the components of <math>R</math> enumerated above.

In the case of a circuit resistors, the loop rule might look something like:
<math> |emf| = I_{1}R_{1} + I_{2}R_{2}</math>

==Equations Derived==
From the definition of resistance and the voltage potential formula discussed above, a number of useful equations can be derived and solved.
The first equation is <math> v = uE</math> where <math> E </math> is electron field , <math> u</math> as electron mobility, and <math> v</math> is drift speed.

This equation offers insight into the microscopic view of the resistor.

The second equation that can be derived is <math> I = |q|nAv</math>.
This equation can be used, in addition to the above equation <math> I = \frac{ΔV}{R}</math> to solve for macroscopic properties of the resistor.

==Example Problems==
===Easy Example===

'''Question:'''
Use the loop rule to calculate the voltage drop across each resistor. Then ensure that your answer is correct.
[[File:EasyExample.JPG]]

'''Answer:'''

[[File:EasyExampleAnswerResize.jpg]]

==Applications==

'''1.How is this topic connected to something that you are interested in?''' I am very interested in computers and I know that circuitry is the foundation of computers and other electronic equipment.

'''2.How is it connected to your major?''' My major is Industrial Engineering, and although I won't study resistors directly in any of my classes, I understand that resistors are crucial in the creation of the tools all engineers and scientists use such as computers and calculators.

'''3.Is there an interesting industrial application?''' As stated above, resistors are widely used in electric circuits. They are used to reduce current flow, change signal levels, and terminate transmission.

==Bibliography==
<references> http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html <references/>

R Circuit

2017-11-24T22:00:40Z

MattMunns: /* Easy Example */

Claimed by Matthew Munns - Fall 2017

Resistors may exist in a circuit and resist electric charge. The resistance of a resistor depends on the properties of the material and the area of the resistor. These two attributes will be investigated later in the page.

Resistors may be ohmic or non-ohmic. An ohmic resistor has a conductivity that is nearly constant, while a non-ohmic resistor will vary depending on the conditions. This page will focus on ohmic resistors in a complex circuit.

The following is an image of an ohmic resistor like the resistor used in lab:
[[File:ResistorResize.jpg]]
==History==
Georg Simon Ohm, born in 1789, discovered Ohm's law. This law relates the current, voltage, and resistance across a resistor. His law was widely accepted by 1850. Ohm's law became the fundamental law in circuit analysis. In 1959, inventor Otis Boykin filed a patent for a resistor that allows manufacturers to designate a value of resistance for a piece of wire in equipment. In 1962, he patented an improved version, which could withstand more extreme conditions. This reduced the cost and increased the reliability of a variety of electronic products. <ref>{{cite web|work=The Philadelphia Tribune|title=Otis Boykin: Invented an Improved Electrical Resistor| publisher=The Philadelphia Tribune|url=http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html}}</ref>

==Mathematics==

As discussed above, resistance of a material is dependent on two factors: the properties of the material, and the area of the resistor.

From the above factors, we get the following definition of resistance:
<math>R = \frac{L}{σ A}</math>

In this definition <math> L </math> is the length of the resistor, <math> A </math> is the cross-sectional area of the resistor, and <math> σ </math> is the conductivity of the material.
<math> σ </math> can be further broken down to show <math> σ = |q|nu </math>.

==In A Circuit==

There is a change in potential energy across a resistor, which is useful when evaluating the loop rule in a circuit with resistors. The change in potential across a resistor is <math> I = \frac{ΔV}{R} </math>
Knowing this equation allows one to solve for <math> ΔV </math> if given <math>I</math> and either <math>R</math> or the components of <math>R</math> enumerated above.

In the case of a circuit resistors, the loop rule might look something like:
<math> |emf| = I_{1}R_{1} + I_{2}R_{2}</math>

==Equations Derived==
From the definition of resistance and the voltage potential formula discussed above, a number of useful equations can be derived and solved.
The first equation is <math> v = uE</math> where <math> E </math> is electron field , <math> u</math> as electron mobility, and <math> v</math> is drift speed.

This equation offers insight into the microscopic view of the resistor.

The second equation that can be derived is <math> I = |q|nAv</math>.
This equation can be used, in addition to the above equation <math> I = \frac{ΔV}{R}</math> to solve for macroscopic properties of the resistor.

==Example Problems==
===Easy Example===
[[File:EasyExample.JPG]]

'''Question:'''
Use the loop rule to calculate the voltage drop across each resistor. Then ensure that your answer is correct.

'''Answer:'''

[[File:EasyExampleAnswerResize.jpg]]

==Applications==

'''1.How is this topic connected to something that you are interested in?''' I am very interested in computers and I know that circuitry is the foundation of computers and other electronic equipment.

'''2.How is it connected to your major?''' My major is Industrial Engineering, and although I won't study resistors directly in any of my classes, I understand that resistors are crucial in the creation of the tools all engineers and scientists use such as computers and calculators.

'''3.Is there an interesting industrial application?''' As stated above, resistors are widely used in electric circuits. They are used to reduce current flow, change signal levels, and terminate transmission.

==Bibliography==
<references> http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html <references/>

R Circuit

2017-11-24T22:00:11Z

MattMunns:

Claimed by Matthew Munns - Fall 2017

Resistors may exist in a circuit and resist electric charge. The resistance of a resistor depends on the properties of the material and the area of the resistor. These two attributes will be investigated later in the page.

Resistors may be ohmic or non-ohmic. An ohmic resistor has a conductivity that is nearly constant, while a non-ohmic resistor will vary depending on the conditions. This page will focus on ohmic resistors in a complex circuit.

The following is an image of an ohmic resistor like the resistor used in lab:
[[File:ResistorResize.jpg]]
==History==
Georg Simon Ohm, born in 1789, discovered Ohm's law. This law relates the current, voltage, and resistance across a resistor. His law was widely accepted by 1850. Ohm's law became the fundamental law in circuit analysis. In 1959, inventor Otis Boykin filed a patent for a resistor that allows manufacturers to designate a value of resistance for a piece of wire in equipment. In 1962, he patented an improved version, which could withstand more extreme conditions. This reduced the cost and increased the reliability of a variety of electronic products. <ref>{{cite web|work=The Philadelphia Tribune|title=Otis Boykin: Invented an Improved Electrical Resistor| publisher=The Philadelphia Tribune|url=http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html}}</ref>

==Mathematics==

As discussed above, resistance of a material is dependent on two factors: the properties of the material, and the area of the resistor.

From the above factors, we get the following definition of resistance:
<math>R = \frac{L}{σ A}</math>

In this definition <math> L </math> is the length of the resistor, <math> A </math> is the cross-sectional area of the resistor, and <math> σ </math> is the conductivity of the material.
<math> σ </math> can be further broken down to show <math> σ = |q|nu </math>.

==In A Circuit==

There is a change in potential energy across a resistor, which is useful when evaluating the loop rule in a circuit with resistors. The change in potential across a resistor is <math> I = \frac{ΔV}{R} </math>
Knowing this equation allows one to solve for <math> ΔV </math> if given <math>I</math> and either <math>R</math> or the components of <math>R</math> enumerated above.

In the case of a circuit resistors, the loop rule might look something like:
<math> |emf| = I_{1}R_{1} + I_{2}R_{2}</math>

==Equations Derived==
From the definition of resistance and the voltage potential formula discussed above, a number of useful equations can be derived and solved.
The first equation is <math> v = uE</math> where <math> E </math> is electron field , <math> u</math> as electron mobility, and <math> v</math> is drift speed.

This equation offers insight into the microscopic view of the resistor.

The second equation that can be derived is <math> I = |q|nAv</math>.
This equation can be used, in addition to the above equation <math> I = \frac{ΔV}{R}</math> to solve for macroscopic properties of the resistor.

==Example Problems==
===Easy Example===
[[File:EasyExample.JPG]]

Question:
Use the loop rule to calculate the voltage drop across each resistor. Then ensure that your answer is correct.

Answer:
[[File:EasyExampleAnswerResize.jpg]]

==Applications==

'''1.How is this topic connected to something that you are interested in?''' I am very interested in computers and I know that circuitry is the foundation of computers and other electronic equipment.

'''2.How is it connected to your major?''' My major is Industrial Engineering, and although I won't study resistors directly in any of my classes, I understand that resistors are crucial in the creation of the tools all engineers and scientists use such as computers and calculators.

'''3.Is there an interesting industrial application?''' As stated above, resistors are widely used in electric circuits. They are used to reduce current flow, change signal levels, and terminate transmission.

==Bibliography==
<references> http://www.phillytrib.com/otis-boykin-invented-an-improved-electrical-resistor/article_f73aeede-4d70-5ea2-90c6-4d8b7b93e3e1.html <references/>

2017-11-24T21:37:33Z

MattMunns: /* Easy Example */

Claimed by Matthew Munns - Fall 2017

Resistors may exist in a circuit and resist electric charge. The resistance of a resistor depends on the properties of the material and the area of the resistor. These two attributes will be investigated later in the page.

Resistors may be ohmic or non-ohmic. An ohmic resistor has a conductivity that is nearly constant, while a non-ohmic resistor will vary depending on the conditions. This page will focus on ohmic resistors in a complex circuit.

The following is an image of an ohmic resistor like the resistor used in lab:
[[File:Resistor3.jpg]]
==History==
Georg Simon Ohm, born in 1789, discovered Ohm's law. This law relates the current, voltage, and resistance across a resistor. His law was widely accepted by 1850. Ohm's law became the fundamental law in circuit analysis.

==Mathematics==

As discussed above, resistance of a material is dependent on two factors: the properties of the material, and the area of the resistor.

From the above factors, we get the following definition of resistance:
<math>R = \frac{L}{σ A}</math>

In this definition <math> L </math> is the length of the resistor, <math> A </math> is the cross-sectional area of the resistor, and <math> σ </math> is the conductivity of the material.
<math> σ </math> can be further broken down to show <math> σ = |q|nu </math>.

==In A Circuit==

There is a change in potential energy across a resistor, which is useful when evaluating the loop rule in a circuit with resistors. The change in potential across a resistor is <math> I = \frac{ΔV}{R} </math>
Knowing this equation allows one to solve for <math> ΔV </math> if given <math>I</math> and either <math>R</math> or the components of <math>R</math> enumerated above.

==Equations Derived==
From the definition of resistance and the voltage potential formula discussed above, a number of useful equations can be derived and solved.
The first equation is <math> v = uE</math> where <math> E </math> is electron field , <math> u</math> as electron mobility, and <math> v</math> is drift speed.

This equation offers insight into the microscopic view of the resistor.

The second equation that can be derived is <math> I = |q|nAv</math>.
This equation can be used, in addition to the above equation <math> I = \frac{ΔV}{R}</math> to solve for macroscopic properties of the resistor.

==Example Problems==
===Easy Example===
[[File:EasyExample.JPG]]

Question:
Use the loop rule to calculate the voltage drop across each resistor. Then ensure that your answer is correct.

Answer:
[[File:EasyExampleAnswerResize.jpg]]

==Applications==

'''1.'''How is this topic connected to something that you are interested in? I am very interested in computers and I know that circuitry is the foundation of computers and other electronic equipment.

'''2.'''How is it connected to your major? My major is Industrial Engineering, and although I won't study resistors directly in any of my classes, I understand that resistors are crucial in the creation of the tools all engineers and scientists use such as computers and calculators.

'''3.'''Is there an interesting industrial application? As stated above, resistors are widely used in electric circuits. They are used to reduce current flow, change signal levels, and terminate transmission.

File:EasyExampleAnswerResize.jpg

2017-11-24T21:37:10Z

MattMunns:

R Circuit

2017-11-24T21:36:02Z

MattMunns: /* Applications */

Claimed by Matthew Munns - Fall 2017

Resistors may exist in a circuit and resist electric charge. The resistance of a resistor depends on the properties of the material and the area of the resistor. These two attributes will be investigated later in the page.

Resistors may be ohmic or non-ohmic. An ohmic resistor has a conductivity that is nearly constant, while a non-ohmic resistor will vary depending on the conditions. This page will focus on ohmic resistors in a complex circuit.

The following is an image of an ohmic resistor like the resistor used in lab:
[[File:Resistor3.jpg]]
==History==
Georg Simon Ohm, born in 1789, discovered Ohm's law. This law relates the current, voltage, and resistance across a resistor. His law was widely accepted by 1850. Ohm's law became the fundamental law in circuit analysis.

==Mathematics==

As discussed above, resistance of a material is dependent on two factors: the properties of the material, and the area of the resistor.

From the above factors, we get the following definition of resistance:
<math>R = \frac{L}{σ A}</math>

In this definition <math> L </math> is the length of the resistor, <math> A </math> is the cross-sectional area of the resistor, and <math> σ </math> is the conductivity of the material.
<math> σ </math> can be further broken down to show <math> σ = |q|nu </math>.

==In A Circuit==

There is a change in potential energy across a resistor, which is useful when evaluating the loop rule in a circuit with resistors. The change in potential across a resistor is <math> I = \frac{ΔV}{R} </math>
Knowing this equation allows one to solve for <math> ΔV </math> if given <math>I</math> and either <math>R</math> or the components of <math>R</math> enumerated above.

==Equations Derived==
From the definition of resistance and the voltage potential formula discussed above, a number of useful equations can be derived and solved.
The first equation is <math> v = uE</math> where <math> E </math> is electron field , <math> u</math> as electron mobility, and <math> v</math> is drift speed.

This equation offers insight into the microscopic view of the resistor.

The second equation that can be derived is <math> I = |q|nAv</math>.
This equation can be used, in addition to the above equation <math> I = \frac{ΔV}{R}</math> to solve for macroscopic properties of the resistor.

==Example Problems==
===Easy Example===
[[File:EasyExample.JPG]]

Question:
Use the loop rule to calculate the voltage drop across each resistor. Then ensure that your answer is correct.

Answer:
[[File:EasyExampleAnswer.JPG]]

==Applications==

'''1.'''How is this topic connected to something that you are interested in? I am very interested in computers and I know that circuitry is the foundation of computers and other electronic equipment.

'''2.'''How is it connected to your major? My major is Industrial Engineering, and although I won't study resistors directly in any of my classes, I understand that resistors are crucial in the creation of the tools all engineers and scientists use such as computers and calculators.

'''3.'''Is there an interesting industrial application? As stated above, resistors are widely used in electric circuits. They are used to reduce current flow, change signal levels, and terminate transmission.

R Circuit

R Circuit

2017-11-22T23:25:48Z

MattMunns:

File:Resistor3.jpg

2017-11-22T23:25:28Z

MattMunns: resistor

resistor

R Circuit

2017-11-22T23:24:24Z

MattMunns:

2017-11-22T23:05:48Z

MattMunns:

Claimed and Written by Daniel Kurniawan for PHYS2212

Claimed to update by Matthew Munns - Fall 2017

[[File:Voltages.jpg|right|300px|thumb|The figure above shows a voltmeter measuring the potential difference in the battery]]

[https://en.wikipedia.org/wiki/Voltage Electric Potential Difference], also known as voltage, is the difference in [https://en.wikipedia.org/wiki/Electric_potential electric potential energy] between two points per unit of electric charge. The voltage between two points is equal to the work done per unit of charge against an unchanging electric field to move the charge between two points and is measured in volts.

Voltage can be caused by static [https://en.wikipedia.org/wiki/Electric_field electric fields], by [https://en.wikipedia.org/wiki/Electric_current electric current] through a [https://en.wikipedia.org/wiki/Magnetic_field magnetic field], by time-varying magnetic fields, or some combination of these three. One can use a [https://en.wikipedia.org/wiki/Voltmeter voltmeter] to measure the potential difference between two points in a circuit. A voltage may represent either a source of energy (electromotive force), or lost, used, or stored energy (potential drop).

==Voltage==

===Definition===

Say you have two points "A" and "B" in space. The potential difference is defined as the difference in electric potential between those two points. Electric potential is electric potential energy per unit charge, measured in [https://en.wikipedia.org/wiki/Joule joules] per [https://en.wikipedia.org/wiki/Coulomb coulomb] (J/C), otherwise known as volts.

===Calculating Potential Difference===

<math>\Delta V_{BA} = V(x_B) - V(x_A) = - \int_{r_0}^{x_B} \vec{E} \cdot d\vec{l} - \left( - \int_{r_0}^{x_A} \vec{E} \cdot d\vec{l} \right)
= \int_{x_B}^{r_0} \vec{E} \cdot d\vec{l} + \int_{r_0}^{x_A} \vec{E} \cdot d\vec{l} = \int_{x_B}^{x_A} \vec{E} \cdot d\vec{l}</math>

As seen above, the potential difference from one point to another in space is calculated as the path integral of the electric field and the time rate of change of magnetic field along that path (alternate way - multiply electric field times the distance covered across the two points). The voltage between point A to point B is equal to the work which would have to be done, per unit charge, against or by the electric field to move the charge from A to B. The voltage between the two ends of a path is the total energy required to move a small electric charge along that path, divided by the magnitude of the charge. Both an unchanging electric field and a dynamic electromagnetic field must be included in determining the voltage between two points. Check out this [https://www.youtube.com/watch?v=Ircup9aIJzU YouTube Video] that shows how to calculate potential, potential difference, and voltage in a system.

Potential difference is defined in such a way that negatively charged objects are pulled towards higher voltages, while positively charged objects are attracted towards lower voltages. This means that the [https://en.wikipedia.org/wiki/Electric_current#Current conventional current] in a system always flows from higher voltage to lower voltage. Current can flow from lower voltage to higher voltage, but only when there is some source of energy present to push it against the opposing electric field. For example, inside a [https://en.wikipedia.org/wiki/Battery_(electricity) battery], chemical reactions provide the energy needed for ion current to flow from the negative to the positive terminal.

==Applications==

===Circuits===

Potential difference is typically used in describing the voltage dropped across some sort of electrical device, such as a [https://en.wikipedia.org/wiki/Resistor resistor]. The voltage drop across the device is the difference between measurements at each terminal of the device with respect to a common reference point. The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing magnetic field have a voltage of zero. Any two points with the same potential may be connected by a conductor and no current will flow between them.

====Potential Difference in a Series Circuit====

[[File: Seriess.jpg]]

In a [https://en.wikipedia.org/wiki/Series_and_parallel_circuits series circuit], the potential difference supplied by the battery is divided up between the components. If the components all have the same resistance they will have equal amounts of potential difference across them. If the resistances are not equal, they may have different amounts of potential difference (See [https://en.wikipedia.org/wiki/Ohm%27s_law Ohm's Law]) across them but when added up they must always equal the potential difference supplied by the battery.

====Potential Difference in a Parallel Circuit====

[[File: Parallel.jpg]]

In a [https://en.wikipedia.org/wiki/Series_and_parallel_circuits parallel circuit],The potential difference supplied by the battery is the same potential difference as that across each component in the parallel circuit. If three resistors are placed in parallel branches and powered by a 12-volt battery, then the voltage drop across each one of the three resistors is 12 volts. A charge flowing through the circuit would only encounter one of these three resistors and thus encounter a single voltage drop of 12 volts.

===Kirchoff's Voltage Law===

One of [https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws Kirchoff's Circuit Laws] (more specifically the Voltage Law) can be used to calculate the various voltages within a circuit. For example, the voltage between points A and C is the sum of the voltage between A and B and the voltage between B and C. The various voltages can be calculated using [https://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.KVL.html Kirchoff's Voltage Law], which states that the directed sum of the electrical potential differences around any closed network is zero. Essentially, the sum of the potential differences in any closed loop is equivalent to the sum of the potential drops in that loop.

<math>\sum_{k=1}^n V_k = 0</math>

'''Example:'''

[[File: 9.png]]

In the figure above, the total voltage around loop 1 should sum to zero, as does the total voltage in loop 2. Also, the loop which consists of the outer part of the circuit (the path ABCD) should also sum to zero, as shown by Kirchoff's Voltage Law.

==See Also==
[https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws Kirchoff's Circuit Laws] <div></div>
[https://en.wikipedia.org/wiki/Alternating_current Alternating Current]<div></div>
[https://en.wikipedia.org/wiki/Direct_current Direct Current]<div></div>
[https://en.wikipedia.org/wiki/Electric_potential Electric Potential]<div></div>
[https://en.wikipedia.org/wiki/Ohm%27s_law Ohm's Law]

===External Readings===
[https://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.KVL.html Kirchoff's Voltage Law]<div></div>
[http://www.physicsclassroom.com/class/circuits/Lesson-1/Electric-Potential-Difference Electric Potential Difference]

===YouTube Videos===
[https://www.youtube.com/watch?v=Ircup9aIJzU Calculating Potential, Potential Difference, and Voltage]<div></div>
[https://www.youtube.com/watch?v=HJrkw_YQzcc Potential Difference as a Path Integral]

==References==
[https://en.wikipedia.org/wiki/Voltage Voltage]<div></div>
[http://www.physicsclassroom.com/class/circuits/Lesson-1/Electric-Potential-Difference Potential Difference]<div></div>
[http://www.schoolphysics.co.uk/age16-19/Electricity%20and%20magnetism/Current%20electricity/text/Potential_and_potential_difference/index.html Potential and Potential Difference]<div></div>
[http://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits Circuits]