Difference between revisions of "Current and Resistance"
(Created page with "= Textbook = [https://openstax.org/books/university-physics-volume-2/pages/9-introduction University Physics Volume 2: Chapter 9] = Current and Resistance = == Theory == <youtube>FViTaHwLgxo</youtube> <youtube>nmA7xmXwXqg</youtube> <br class="clear"/>") |
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Back to [[Electricity_and_Magnetism]] | |||
= Textbook = | |||
[https://openstax.org/books/university-physics-volume-2/pages/9-introduction University Physics Volume 2: Chapter 9] | |||
= Current and Resistance = | |||
== Theory == | |||
=== Current and Current Density === | |||
Electric current (<math>I</math>) is the flow of electric charge through a conductor, measured in amperes (<math>A</math>). The current density (<math>\vec{J}</math>) represents the current per unit cross-sectional area, expressed as: | |||
<math>\vec{J} = \frac{\vec{I}}{A} = \sigma \vec{E}</math> | |||
where <math>\sigma</math> is the conductivity, and <math>\vec{E}</math> is the electric field. | |||
<youtube>FViTaHwLgxo</youtube> | |||
<youtube>1ahlvmI_0HU</youtube> | |||
=== Resistance, Resistivity, and Conductivity === | |||
Resistance (<math>R</math>) quantifies the opposition to the flow of current in a conductor, measured in ohms (<math>\Omega</math>). Resistivity (<math>\rho</math>) is a material property that measures resistance per unit length and cross-sectional area. Conductivity (<math>\sigma</math>) is the inverse of resistivity. | |||
<math>R = \rho \frac{L}{A}, \quad \sigma = \frac{1}{\rho}</math> | |||
where <math>L</math> is the length of the conductor and <math>A</math> is its cross-sectional area. | |||
<youtube>FFHUoWFtab0</youtube> | |||
<youtube>IWTyLsvQmxE</youtube> | |||
=== Ohm's Law === | |||
Ohm's Law relates the voltage (<math>V</math>), current (<math>I</math>), and resistance (<math>R</math>) in a circuit: | |||
<math>V = IR</math> | |||
It also applies at the microscopic level: | |||
<math>\vec{E} = \rho \vec{J}</math> | |||
<youtube>nmA7xmXwXqg</youtube> | |||
<br class="clear"/> | |||
==== Ohm's Law Simulation ==== | |||
*[https://phet.colorado.edu/en/simulations/ohms-law Ohm's Law on PhET] <br> | |||
Back to [[Electricity_and_Magnetism]] | |||
= Textbook = | = Textbook = | ||
[https://openstax.org/books/university-physics-volume-2/pages/9-introduction University Physics Volume 2: Chapter 9] | [https://openstax.org/books/university-physics-volume-2/pages/9-introduction University Physics Volume 2: Chapter 9] | ||
Line 4: | Line 46: | ||
= Current and Resistance = | = Current and Resistance = | ||
== Theory == | == Theory == | ||
=== Current and Current Density === | |||
Electric current (<math>I</math>) is the flow of electric charge through a conductor, measured in amperes (<math>A</math>). The current density (<math>\vec{J}</math>) represents the current per unit cross-sectional area, expressed as: | |||
<math>\vec{J} = \frac{\vec{I}}{A} = \sigma \vec{E}</math> | |||
where <math>\sigma</math> is the conductivity, and <math>\vec{E}</math> is the electric field. | |||
<math>I = \int \vec{J} \cdot d\vec{A}</math> | |||
<youtube>FViTaHwLgxo</youtube> | <youtube>FViTaHwLgxo</youtube> | ||
<youtube>1ahlvmI_0HU</youtube> | |||
=== Resistance, Resistivity, and Conductivity === | |||
Resistance (<math>R</math>) quantifies the opposition to the flow of current in a conductor, measured in ohms (<math>\Omega</math>). Resistivity (<math>\rho</math>) is a material property that measures resistance per unit length and cross-sectional area. Conductivity (<math>\sigma</math>) is the reciprocal of resistivity. | |||
<math>R = \rho \frac{L}{A}, \quad \sigma = \frac{1}{\rho}</math> | |||
where <math>L</math> is the length of the conductor and <math>A</math> is its cross-sectional area. | |||
<youtube>FFHUoWFtab0</youtube> | |||
<youtube>IWTyLsvQmxE</youtube> | |||
=== Ohm's Law === | |||
Ohm's Law relates the voltage (<math>V</math>), current (<math>I</math>), and resistance (<math>R</math>) in a circuit: | |||
<math>V = IR</math> | |||
It also applies at the microscopic level: | |||
<math>\vec{E} = \rho \vec{J}</math> | |||
<youtube>nmA7xmXwXqg</youtube> | <youtube>nmA7xmXwXqg</youtube> | ||
<br class="clear"/> | |||
==== Ohm's Law Simulation ==== | |||
*[https://phet.colorado.edu/en/simulations/ohms-law Ohm's Law on PhET] <br> | |||
<br class="clear"/> | |||
Back to [[Electricity_and_Magnetism]] | |||
<br class="clear"/> | <br class="clear"/> | ||
Next: [[Notes on DC Circuits]] |
Latest revision as of 15:47, 22 November 2024
Back to Electricity_and_Magnetism
Textbook
University Physics Volume 2: Chapter 9
Current and Resistance
Theory
Current and Current Density
Electric current () is the flow of electric charge through a conductor, measured in amperes (). The current density () represents the current per unit cross-sectional area, expressed as: where is the conductivity, and is the electric field.
Resistance, Resistivity, and Conductivity
Resistance () quantifies the opposition to the flow of current in a conductor, measured in ohms (). Resistivity () is a material property that measures resistance per unit length and cross-sectional area. Conductivity () is the inverse of resistivity.
where is the length of the conductor and is its cross-sectional area.
Ohm's Law
Ohm's Law relates the voltage (), current (), and resistance () in a circuit:
It also applies at the microscopic level:
Ohm's Law Simulation
Back to Electricity_and_Magnetism
Textbook
University Physics Volume 2: Chapter 9
Current and Resistance
Theory
Current and Current Density
Electric current () is the flow of electric charge through a conductor, measured in amperes (). The current density () represents the current per unit cross-sectional area, expressed as: where is the conductivity, and is the electric field.
Resistance, Resistivity, and Conductivity
Resistance () quantifies the opposition to the flow of current in a conductor, measured in ohms (). Resistivity () is a material property that measures resistance per unit length and cross-sectional area. Conductivity () is the reciprocal of resistivity.
where is the length of the conductor and is its cross-sectional area.
Ohm's Law
Ohm's Law relates the voltage (), current (), and resistance () in a circuit:
It also applies at the microscopic level:
Ohm's Law Simulation
Back to Electricity_and_Magnetism
Next: Notes on DC Circuits