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Question:

Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons?

Solution:

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=(eE/m)T
E= field
m=mass of electron
T= Relaxation time
From this, you can find the expression for relaxation time
T=vm/(eE)
Field is E=V/L, where L=Length and V=IR.
From this you can modify the expression in terms of resistivity.