SUMMARY

The current in a conductor is $I=dQ/dt$, where dQ is the charge crossing a cross-section in time interval dt; the SI unit of current is the ampere, $1\ \text{A}=1\ \text{C s}^{-1}$. The current density J in a conductor is the current per unit area, $J=I/A$; current is a scalar, but current density is a vector. The general (microscopic) form of Ohm's law is $\vec J=\sigma\vec E$. The practical (macroscopic) form of Ohm's law states $V\propto I$, i.e. $V=IR$, where R is resistance and V is the potential difference across the conductor's ends. Resistance is $R=V/I$, SI unit ohm ($\Omega$), $1\ \Omega = 1\ \text{V/A}$; also $R=\rho l/A$, where l is the conductor's length and A its cross-sectional area. Resistivity is the material property that determines how much resistance a given material offers to current flow. …