Current and Resistance

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Textbook

University Physics Volume 2: Chapter 9

Current and Resistance

Theory

Current and Current Density

Electric current ($I$) is the flow of electric charge through a conductor, measured in amperes ($A$). The current density ($\overrightarrow{J}$) represents the current per unit cross-sectional area, expressed as: $\overrightarrow{J}=\frac{\overrightarrow{I}}{A}=\sigma \overrightarrow{E}$ where $\sigma$ is the conductivity, and $\overrightarrow{E}$ is the electric field.

Resistance, Resistivity, and Conductivity

Resistance ($R$) quantifies the opposition to the flow of current in a conductor, measured in ohms ($\mathrm{\Omega }$). Resistivity ($\rho$) is a material property that measures resistance per unit length and cross-sectional area. Conductivity ($\sigma$) is the inverse of resistivity.

$R=\rho \frac{L}{A},\sigma =\frac{1}{\rho }$

where $L$ is the length of the conductor and $A$ is its cross-sectional area.

Ohm's Law

Ohm's Law relates the voltage ($V$), current ($I$), and resistance ($R$) in a circuit: $V=IR$

It also applies at the microscopic level: $\overrightarrow{E}=\rho \overrightarrow{J}$

Ohm's Law Simulation

• Ohm's Law on PhET
  

Back to Electricity_and_Magnetism

Textbook

University Physics Volume 2: Chapter 9

Current and Resistance

Theory

Current and Current Density

Electric current ($I$) is the flow of electric charge through a conductor, measured in amperes ($A$). The current density ($\overrightarrow{J}$) represents the current per unit cross-sectional area, expressed as: $\overrightarrow{J}=\frac{\overrightarrow{I}}{A}=\sigma \overrightarrow{E}$ where $\sigma$ is the conductivity, and $\overrightarrow{E}$ is the electric field.

$I=\int \overrightarrow{J}\cdot d\overrightarrow{A}$

Resistance, Resistivity, and Conductivity

Resistance ($R$) quantifies the opposition to the flow of current in a conductor, measured in ohms ($\mathrm{\Omega }$). Resistivity ($\rho$) is a material property that measures resistance per unit length and cross-sectional area. Conductivity ($\sigma$) is the reciprocal of resistivity.

$R=\rho \frac{L}{A},\sigma =\frac{1}{\rho }$

where $L$ is the length of the conductor and $A$ is its cross-sectional area.

Ohm's Law

Ohm's Law relates the voltage ($V$), current ($I$), and resistance ($R$) in a circuit: $V=IR$

It also applies at the microscopic level: $\overrightarrow{E}=\rho \overrightarrow{J}$

Ohm's Law Simulation

• Ohm's Law on PhET
  

Back to Electricity_and_Magnetism
Next: Notes on DC Circuits