OpenStax University Physics/E&M/Current and Resistance

For quiz at QB/d_cp2.9
Electric current: 1 Amp (A) = 1 Coulomb (C) per second (s)

Current=$$I=dQ/dt=nqv_dA$$, where

$$(n,q,v_d,A)$$ = (density, charge, speed, Area)

$$I=\int\vec J\cdot d\vec A$$ where $$\vec J = nq\vec v_d $$ =current density.

$$\vec E= \rho\vec J$$ = electric field where $$\rho$$ = resistivity

$$\rho=\rho_0\left[1+\alpha (T-T_0)\right]$$, and $$R=R_0\left[1+\alpha \Delta T\right]$$,

where $$R=\rho \tfrac L A$$ is resistance

$$V=IR$$ and Power=$$P=IV=I^2R=V^2/R$$