Define current density and relaxation time. Derive an expression for resistivity of a conductor in terms of number density of charge carriers in the conductor and relaxation time.

Definition ofCurrent density is defined as the current flowing per unit area of cross section of a conductor.Relaxation time is the average time interval between two successive collisions for drifting electrons in a conductor. From \(\displaystyle \mathrm{I}=n A e v_{d}\) \[\text { but } \begin{aligned} v_{d} & =\frac{e E}{m} \tau \\ \therefore & \mathrm{I}=n A e . \frac{e E}{m} \tau \end{aligned} \]