Current density: Current density is the current per unit area of cross-section of a conductor.
$\mathit{J}=\frac{\mathit{I}}{\mathit{A}}$
Relaxation time: Relaxation time is the time interval between two successive collisions of electrons in a conductor.
Expression for resistivity:
${\mathit{v}}_{\mathit{d}}=\frac{\mathit{e}\mathrm{E}}{\mathit{m}}\mathit{\tau }$
or,
or, $\mathit{V}=\frac{{\mathit{v}}_{\mathit{d}}\mathit{m}\mathit{l}}{\mathit{e}\mathit{\tau }}$
or, $\mathit{I}\mathit{R}=\frac{{\mathit{v}}_{\mathit{d}}\mathit{m}\mathit{l}}{\mathit{e}\mathit{\tau }}$ (since from Ohm's law, $\mathit{V}=\mathit{I}\mathit{R}$ )
or, $\mathit{R}=\frac{{\mathit{v}}_{\mathit{d}}\mathit{m}\mathit{l}}{\mathit{e}\mathit{\tau }\mathit{I}}$

$\mathit{\rho }=\frac{{\mathit{v}}_{\mathit{d}}\mathit{m}\mathit{A}}{\mathit{e}\mathit{\tau }\mathit{I}}$
$$

$\therefore \mathit{\rho }=\frac{\mathit{m}}{\mathit{n}{\mathit{e}}^2\mathit{\tau }}$