Question

The relaxation time τ is nearly independent of applied E field whereas it changes significantly with temperature T. First fact is (in part) responsible for Ohm’s law whereas the second fact leads to variation of ρ with temperature. Elaborate why?

Answer 1

Here T,m are relaxation time and mass of electron

As we know.....i=neAv v is drift velocityv=((-eE)/m)*TSince,E=-V/lOn putting these valuesi=(ne^2ATV)/(ml)As P=RA/lHere,P is resistivitySince,R=ml/(ne^2AlT)Therefore, P=m/(ne^2T)

Thus,change in temperature implies change in T which implies change in resistivity (P)

Answer 2

Explanation:

As the drift velocity increases, the relaxation time ( τ ) (average time betweensuccessive collision) decreases which increases the ρ by formula:

p=

$\frac{m}{ne2}$

The drift velocity (v d ) changes of the order of one mm on increasing electric field, whereasthe drift velocity increases of the order of 10

2

m/s when the number of free electrons (n)increases on increasing temperature (T).

So, due to increase in v

d

the relaxation time ( τ )considerably decreases in metal or conductor.