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: Relaxation time is nothing but the gap of time between two consecutive collisions of electrons in a conductor.

The relationship between the relaxation time (T) and drift velocity (Vd) can be stated as below.

vd=(eEm) T

Where

Vd = drift velocity,

e = charge of electron,

E = field,

m = mass of electron,

T = Relaxation time.

So, the relaxation time (T) can be expressed as:

T=(vdme) E.

Let

L = Length of the conductor,

A = Area of the conductor,

n = current density.

Then current that flows through the conductor will be

I=-neAvd

I=neA eEm T

I=ne²EAmT

I=ne²VAmLT

VI=mLne²TA

R=mne²TLA

R=ρLA

Field E will then, be

E = V/L.

Then, using Ohm’s law, the current that flows through the conductor becomes:

V = IR,

R = V/I.