Engineering Physics

5.3 Relaxation time, mean free path, mean collision time and drift velocity

(i) Relaxation time (τ): In the absence of an external electric field, the free electrons in a metallic substance will move in random directions, so that the resultant velocity of free electrons in any direction is equal to zero. By applying an external electric field on the specimen, the free electrons of the metal acquire a constant resultant velocity in the opposite direction to that of the applied electric field. If the field is turned off suddenly at t = 0, then the average drift velocity <v_x>0 reduces exponentially to zero. The drift velocity after some time ‘t’ is:

where τ is called relaxation time. when t = τ then Equation (5.20) becomes:

Thus, relaxation ...