Question

Define relaxation time , derive the expression for electrical conductivity of a material in terms of relaxation time

Answer 1

Relaxation Time:

It is the time between two successive collisions between electrons when current flows through the conductor.

Expression for Conductance:

The relation for drift velocity is given by  

Vd = eET/m

And the current through the conductor will be,

I = neAVd = n e^2 A(ET/m)

As, the electric field E is equal to V/L

So,

I = ne^2A(VT/Lm)

I/V = ne^2A(T/Lm)

R = Lm/ ne^2AT

Since, Resistivity = R A/L

Replacing 'R' in Resistivity's expression:

Resistivity = (Lm/ ne^2AT)(A/L)

Resistivity = m/ne^2T

Conductivity = n*e^2*T/m