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 (${\vec {J}}$) represents the current per unit cross-sectional area, expressed as: ${\vec {J}}={\frac {\vec {I}}{A}}=\sigma {\vec {E}}$ where $\sigma$ is the conductivity, and ${\vec {E}}$ is the electric field.

Resistance, Resistivity, and Conductivity

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

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

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: ${\vec {E}}=\rho {\vec {J}}$

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 (${\vec {J}}$) represents the current per unit cross-sectional area, expressed as: ${\vec {J}}={\frac {\vec {I}}{A}}=\sigma {\vec {E}}$ where $\sigma$ is the conductivity, and ${\vec {E}}$ is the electric field.

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

Resistance, Resistivity, and Conductivity

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

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

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: ${\vec {E}}=\rho {\vec {J}}$

Ohm's Law Simulation

• Ohm's Law on PhET
  

Back to Electricity_and_Magnetism
Next: Notes on DC Circuits