Question

Define relaxation time of the free electrons drifting in a conductor: How is it related to the drift velocity of free electrons? Use this relation to deduce the expression for the electrical resistivity of the material.

Answer 1

Relaxation time is the time interval between two successive collisions of electrons in a conductor, when current flows.

$I=current$

$n$ = no. of free electrons

$a$=area of conductor

$v$=drift velocity

$e$=charge of electron

$v=\left(e\frac{E}{m}\right)T$ $E$= field $m$=mass of electron $T$= Relaxation time

From this, you can find expression of relaxation time

$T=v\frac{m}{e}E$

Field is $\frac{V}{L}$ L=Length and $V=IR.$

From this you can modify the expression in terms of resistivity.