The relaxation time τ is nearly independent

Question:

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

Solution:

Relaxation time is the time interval between two successive collisions of the electrons.

It is defined as

τ = mean free path/rms velocity of electrons

Usually, the drift velocity of the electrons is small because there is a frequent collision between the electrons.

ρ = 1/σ = m/ne2τ

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