Physics Book - User contributions [en]

Resistivity

2016-04-14T02:37:52Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Res1.jpg]]

[[File:Res2.jpg]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]
(http://avstop.com/ac/Aviation_Maintenance_Technician_Handbook_General/images/fig10-41.jpg)
===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Scope==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T06:54:34Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Res1.jpg]]

[[File:Res2.jpg]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Scope==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T06:54:00Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Res1.jpg]]

[[File:Res2.jpg]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T06:53:43Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Res2.jpg]]

[[File:Res1.jpg]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

File:Res1.jpg

2016-04-13T06:53:19Z

Clee441:

File:Res2.jpg

2016-04-13T06:52:52Z

Clee441:

Resistivity

2016-04-13T06:50:27Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Resistivity1.JPG | upright=0.56]]

[[File:Resistivity2.jpeg | upright=0.56]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T06:48:06Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Resistivity1.JPG]]

[[File:Resistivity2.jpeg]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T06:47:03Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Resistivity1.JPG]]

[[File:Resistivity2.JPEG]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T06:46:12Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:Resistivity1.JPG]]

[[File:resistivity2.jpg]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T06:45:37Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

[[File:resistivity1.jpg]]

[[File:resistivity2.jpg]]

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

File:Resistivity1.JPG

2016-04-13T06:44:21Z

Clee441:

File:Resistivity2.jpeg

2016-04-13T06:43:52Z

Clee441:

Resistivity

2016-04-13T06:30:50Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}⋅{Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

The definition provided above is specific to ohmic resistors, as stated. These resistors have a uniform cross-section, where current flows uniformly through them. Instead, a more general definition starts with the idea that an electric field inside a specific material is responsible for the electric current flowing within it. Thus, the electrical resistivity, or "p" can be defined as the ratio of the electric field to the density of the current it creates:

:<math>\rho=\frac{E}{J}, \,\!</math>

where "ρ" is the resistivity (ohm⋅meter), "E" is the magnitude of the electric field (volts per meter), and J is the magnitude of the current density (amperes per square meter).

Note, when ''E'' and ''J'' are inside the conductor.
Conductivity is the inverse of resistivity:

:<math>\sigma=\frac{1}{\rho} = \frac{J}{E}. \,\!</math>

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T05:08:53Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}* {Meter})</math> or <math>({Ω}⋅{m})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T05:08:23Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The SI unit of resistivity is often measured in
<math>({Ohm}* {Meter})</math> or <math>({Ω}⋅{m}) and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T05:06:03Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The quantity is often measured in ohms per meter,
<math>({ohm}* {Meter})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T04:57:18Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The quantity is often measured in ohms per meter,
<math>(\frac{Volts}{Amps\ Meter})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables, whereas the Current is the dependent variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resistance can be thought of as a series of pipes. Electrical Resistance in a particular material is similar to an analogy of pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resistivity of the "pipes" never change, but the cross sectional area does, in order for the facilitation of "water" flow (current).

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that is relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivities.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same material at different temperatures may exhibit different resistivities. As materials heat up they become less facilitative of current flow. This is due to the fact that nuclei are moving faster at a sub-atomic level, making it difficult for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder?

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter and is taken outside and left in the sun on a very hot day. What, if anything, will happen to its reading after being outside for a few minutes and why? Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important to electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users cannot expect their circuits to work the same in both nominal and extreme temperature conditions.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T04:50:53Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.
The quantity is often measured in ohms per meter,
<math>(\frac{Volts}{Amps\ Meter})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables and Current is the dependant variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resitance can often be though of as a series of pipes. Electrical Resistance in a particular material is like pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resitivity of the "pipes" never changes. What does change is the cross sectional area making it easier for "water" to pass through.

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that it relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivity.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder.

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter is taken outside and left in the sun on a very hot day. what if anything will happen to its reading after being outside for a few minutes and why. Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users will expect their circuits to work the same whether in a cool air conditioned room or when exposed to extreme temperatures and Electrical Engineers must understand resistivity to know how it will react.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T04:50:26Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.

The quantity is often measured in ohms per meter,
<math>(\frac{Volts}{Amps\ Meter})</math> and is used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables and Current is the dependant variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resitance can often be though of as a series of pipes. Electrical Resistance in a particular material is like pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resitivity of the "pipes" never changes. What does change is the cross sectional area making it easier for "water" to pass through.

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that it relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivity.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder.

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter is taken outside and left in the sun on a very hot day. what if anything will happen to its reading after being outside for a few minutes and why. Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users will expect their circuits to work the same whether in a cool air conditioned room or when exposed to extreme temperatures and Electrical Engineers must understand resistivity to know how it will react.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T04:48:56Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.

This quantity often measured in ohms per meter
<math>(\frac{Volts}{Amps\ Meter})</math> is the equation used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance, copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables and Current is the dependant variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resitance can often be though of as a series of pipes. Electrical Resistance in a particular material is like pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resitivity of the "pipes" never changes. What does change is the cross sectional area making it easier for "water" to pass through.

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that it relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivity.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder.

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter is taken outside and left in the sun on a very hot day. what if anything will happen to its reading after being outside for a few minutes and why. Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users will expect their circuits to work the same whether in a cool air conditioned room or when exposed to extreme temperatures and Electrical Engineers must understand resistivity to know how it will react.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T04:47:14Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.

This quantity often measured in ohms per meter
<math>(\frac{Volts}{Amps\ Meter})</math> is the equation used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Notably, resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is essentially a constant that describes the resistability of a specific material with respect to the current that passes through it. Some materials will more readily allow the flow of current in comparison to others. For instance copper has half the resistivity as that of aluminum. Thus, most wires are made out of copper instead of aluminum -- as aluminum impedes the flow of electrical current.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity, L is the length, and A is the cross-sectional area.

In a circuit the Electrical Resistance is then used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage, '''I''' is the current, and '''R''' is the resistance. In this equations voltage and resistance are independent variables and Current is the dependant variable. This law, while useful, only works for ohmic resistors.

===Water Analogy===
The relationship between resistivity and resitance can often be though of as a series of pipes. Electrical Resistance in a particular material is like pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resitivity of the "pipes" never changes. What does change is the cross sectional area making it easier for "water" to pass through.

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that it relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivity.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder.

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter is taken outside and left in the sun on a very hot day. what if anything will happen to its reading after being outside for a few minutes and why. Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users will expect their circuits to work the same whether in a cool air conditioned room or when exposed to extreme temperatures and Electrical Engineers must understand resistivity to know how it will react.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-13T03:26:28Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of a specific materials ability to impede the flow of an electric current.

This quantity often measured in ohms per meter
<math>(\frac{Volts}{Amps\ Meter})</math> is the equation used to determine the resistance of a given conductor.
Resistivity of an object is almost entirely dependent on two specific factors: temperature and material. Resistivity, unlike resistance, is independent of the size or shape of a material.

==The Main Idea==
Resistivity is in its most basic form a constant for each material that says how easy it is for a current to pass through a given material. Some materials will more easily allow currents to pass through them. For instance it is almost twice as easy to have a current pass through copper as it is for it to pass through aluminum. This explains why most wires are made out of copper instead of aluminum.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity L is the length and A is the cross-sectional area.

In a circuit the Electrical Resistance is then often used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage and '''I''' is the current and '''R''' is the resistance. In this equations voltage and resistance are independent variables and Current is the dependant variable. This law, while useful, only works for certain resistors called ohmic resistors.

===Water Analogy===
The relationship between resistivity and resitance can often be though of as a series of pipes. Electrical Resistance in a particular material is like pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resitivity of the "pipes" never changes. What does change is the cross sectional area making it easier for "water" to pass through.

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that it relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivity.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder.

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter is taken outside and left in the sun on a very hot day. what if anything will happen to its reading after being outside for a few minutes and why. Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users will expect their circuits to work the same whether in a cool air conditioned room or when exposed to extreme temperatures and Electrical Engineers must understand resistivity to know how it will react.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Resistivity

2016-04-09T02:27:25Z

Clee441:

Claimed by Christopher Lee -- Spring 2016
Resistivity is the measure of how difficult it is for a current to pass through a certain material at a certain temperature.

This quantity often measured in ohms per meter or <math>(\frac{Volts}{Amps\ Meter})</math> is used to determine the resistance of a given conductor. Resistivity of an object is almost solely dependent on two factors, temperature and material. Resistivity unlike resistance is independent of the size or shape of a material.

==The Main Idea==
Resistivity is in its most basic form a constant for each material that says how easy it is for a current to pass through a given material. Some materials will more easily allow currents to pass through them. For instance it is almost twice as easy to have a current pass through copper as it is for it to pass through aluminum. This explains why most wires are made out of copper instead of aluminum.

===A Mathematical Model===

Resistance is often calculate from resistivity using the following equation <math>R = \frac{\rho L}{A} </math> where R is the resistance <math>\rho</math> is the resistivity L is the length and A is the cross-sectional area.

In a circuit the Electrical Resistance is then often used to calculate the current in a circuit using the following equation Ohm's law <math>I = \frac{|\Delta V|}{R} </math> where '''V''' is the voltage and '''I''' is the current and '''R''' is the resistance. In this equations voltage and resistance are independent variables and Current is the dependant variable. This law, while useful, only works for certain resistors called ohmic resistors.

===Water Analogy===
The relationship between resistivity and resitance can often be though of as a series of pipes. Electrical Resistance in a particular material is like pipes of varying diameter. The larger the pipe the easier it is for water to get through. The resitivity of the "pipes" never changes. What does change is the cross sectional area making it easier for "water" to pass through.

[[File:Thickness.gif]]

===Resistivity of Materials===
Every conductor has a natural resistivity that it relatively consistent at a given temperature. This number is calculated through experimentation. Here is a list of common conductors and their resistivity.

[[File:Resistivity.jpg]]

===Temperature===
In addition to each material having a different resistivity. The same materials at different temperatures have different resistivities. As materials heat up it becomes harder and harder for current to pass through them. This is because at the sub-atomic level. The nuclei are moving faster making it harder for electrons to move through.

[[File:TemperatureHot.gif]] [[File:TemperatureCold.gif]]

==Examples==

3 examples of potential problems involving resistivity and resistance.

===Simple===
====Question====

An unknown ohmic resistor is attached to a 3V battery and the current is measured at 1 amp. Calculate the resistance of the unknown resistor.

====Answer====

Using the equation I=|dV|/R we can substitute is 1 for I and 3 for dV leaving us with the equation 1=3/R. Solving for R we come to the answer that the it must be a 3 ohm resistor.

===Middling===

====Question====

A cylinder of an unknown material has a resistance of 30 ohms. Another cylinder made of the exact same material is twice as long and has a radius that is twice as large. What is the resistance of this cylinder.

====Answer====
Given the equation <math>R = \frac{\rho L}{A} </math> we know that when the length is doubled the resistance must also double. In addition we know that when the radius is doubled, the cross section area must go up by a factor of 4. This means that the resistance would go down by a factor of 1/4. Putting both of those facts together know that R2 = R1 * 2 * 1/4 or R2 = 15 ohms.

===Difficult===

====Question====

A battery and resistor circuit is connected to a very sensitive ohmmeter is taken outside and left in the sun on a very hot day. what if anything will happen to its reading after being outside for a few minutes and why. Assume the battery is unaffected.

====Answer====

The current would be less that it was inside. Since the circuit was taken outside the resistor would heat up due to the sun. This would in turn cause its resistance to go up. When the resistance goes up and the voltage of the battery stays the same. due to Ohms Law the current must go down, resulting in a lower reading.

==Connectedness==
Resistivity is very important electrical engineers and others who work with circuits because it is important to understand how a circuit is going to work when outside of laboratory conditions. Users will expect their circuits to work the same whether in a cool air conditioned room or when exposed to extreme temperatures and Electrical Engineers must understand resistivity to know how it will react.

== See also ==

*[[Ohm's Law]]
*[[Thin and Thick Wires]]
*[[Current]]

===Further reading===

1. Matter and Interactions by Ruth Chabay and Bruce Sherwood

===External links===

Helpful Links

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.cleanroom.byu.edu/Resistivities.phtml

4. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

5. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

Helpful Videos

1. https://www.youtube.com/watch?v=-PJcj1TCf_g

2. https://www.youtube.com/watch?v=J4Vq-xHqUo8

==References==

1. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

2. http://www.britannica.com/technology/resistance-electronics

3. http://www.nist.gov/data/PDFfiles/jpcrd155.pdf

4. http://www.regentsprep.org/Regents/physics/phys03/bresist/default.htm

5. http://forums.extremeoverclocking.com/showthread.php?p=4144637

[[Category:Simple Circuits]]

Density

2015-11-20T04:45:37Z

Clee441: Density

This topic covers Density -- Claimed by Christopher Lee, M03 Gumbart

==The Main Idea==

Density can be simply defined as the relative compactness of a substance.
The consistency of the matter at hand can be quantified by mass per unit volume.

===A Mathematical Model===

Density = Mass / Volume

The mass can be expressed in grams [g] or kilograms [kg], and the volume is measured in liters [L], cubic centimeters [cm^3], or milliliters [mL].

===A Computational Model===

define mass and volume.
ex:
m = 500
vol = 40
density = m / vol

==Examples==

[[http://www.ssc.education.ed.ac.uk/BSL/pictures/density.jpg]]

==Connectedness==

Density is important in construction of biomaterials that could potentially have clinical applications.

==History==

Archimedes in 250 B.C. "discovered" density. He suspected that he was being cheated on by the metal craftsmen who had constructed his golden crown. Archimedes suspected that the craftsman was using a sizeable amount of silver with his gold crown, which is cheaper, and ultimately an insult to the king. Archimedes put the crown that the craftsmen had created as well as a crown of pure gold both into a bathtub full of water. He measured the amount of water that was in excess and confirmed his suspicions. He then proceeds to chant "Eureka! Eureka!" in the streets.

== See also ==

Mass and Volume Pages.

===Further reading===

physics.info/density

===External links===

http://www.ssc.education.ed.ac.uk/BSL/chemistry/densityd.html

==References==

Chabay & Sherwood: Matters and Interactions -- Modern Mechanics Volume 1, 4th Edition

[[Category:Properties of Matter]]

Main Page

2015-11-20T04:45:05Z

Clee441: /* Properties of Matter */

__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 Catagories ==
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]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[System & Surroundings]]
*[[Newton's First Law of Motion]]
</div>
</div>

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

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

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Michael Faraday]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Marie Curie]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]

</div>
</div>

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

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]

</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Tension]]
* [[Hooke's Law]]
</div>
</div>

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

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* Predicting Change in one dimension
* [[Predicting Change in multiple dimensions]]
* [[Momentum Principle]]
* [[Curving Motion]]
</div>
</div>

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

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Rotation]]
* [[Torque]]
* [[Right Hand Rule]]
* Predicting a Change in Rotation
</div>
</div>

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

===Energy===
<div class="mw-collapsible-content">
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
*[[Work]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Spring Potential Energy]]
</div>
</div>

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

===Collisions===
<div class="mw-collapsible-content">
*[[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]]
*[[Electric Potential]]
**[[Potential Difference in a Uniform Field]]
**[[Sign of Potential Difference]]
*[[Electric Force]]
*[[Polarization]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Bar Magnet]]
**[[Magnetic Force]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
</div>
</div>

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

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
*[[Ohm's Law]]
*[[RC]]
*[[Circular Loop of Wire]]
*[[RL Circuit]]
*[[LC Circuit]]
</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]]
*[[Faraday's Law]]
**[[Inductance]]
*[[Ampere-Maxwell Law]]
</div>
</div>

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

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
</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]]

User talk:Clee441

2015-11-20T04:43:56Z

Clee441:

User talk:Clee441

2015-11-20T04:42:31Z

Clee441: Density