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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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