Key Equations

Average electrical current	$I_{\text{ave}}=\frac{\text{Δ}Q}{\text{Δ}t}$
Definition of an ampere	$1\text{A}=1\text{C/s}$
Electrical current	$I=\frac{dQ}{dt}$
Drift velocity	$v_d=\frac{I}{nqA}$
Current density	$I={\displaystyle \underset{\text{area}}{\iint }\overrightarrow{J}·d\overrightarrow{A}}$
Resistivity	$\rho =\frac{E}{J}$
Common expression of Ohm’s law	$V=IR$
Resistivity as a function of temperature	$\rho ={\rho }_0\left[1+\alpha \left(T-T_0\right)\right]$
Definition of resistance	$R\equiv \frac{V}{I}$
Resistance of a cylinder of material	$R=\rho \frac{L}{A}$
Temperature dependence of resistance	$R=R_0\left(1+\alpha \text{Δ}T\right)$
Electric power	$P=IV$
Power dissipated by a resistor	$P=I^{2}R=\frac{V^2}{R}$