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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?
Solution
Relaxation time is bound to depend on velocities of electrons and ions. Applied electric field affects the velocities of electrons by speeds at the order of 1 mm/s, an insignificant effect. Change in T, on the other hand, affects velocities at the order of 102 m/s. This can affect τ significantly.
[ρ = ρ(E, T) in which E dependence is ignorable for ordinary applied voltages.]
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