Question

(a) Define the terms ‘drift velocity’ and ‘relaxation time’ giving their physical significance.

(b) A conductor of length L is connected across a dc source of emf E. If the conductor is replaced by another of the same material and area of cross-section but of length 5L, by what factor will the drift velocity change?

Answer 1

(a) Drift Velocity: It is the average velocity of the free electrons with which they get drifted towards the positive terminal under the influence of the external field.

Significance: The net current flowing through any cross-section is controlled by drift velocity and there is no transport of charges in a direction perpendicular to the applied field.

Relaxation Time (τ): The average time between successive collisions of electrons or ions in a conductor is called relaxation time.

Significance: It determines the drift velocity acquired by the electrons under the given applied electric force and also determines the electrical conductivity of a conductor at different temperatures.

(b) In first case:

v_d = \(\frac{eV}{mL}\tau\)

In second case:

v'd = \(\frac{eV\tau}{m5L}\)

v'd = \(\frac{1}{5} (\frac{eV}{mL}\tau) = \frac{v_d}{5}\)

Thus we find that the drift velocity becomes \(\frac{1}{5}\)  of its original value.