Relaxation time (τ): It is the time interval which a free electron, on the average, spends between two successive collisions between electrons and ions in the lattice of a conductor.
Relaxation time,
τ = \(\frac{\text{ mean free path }}{\text{ r.m.s. velocity of electron }}\)
or τ = \(\frac{\lambda}{v_{rms}}\)
As the temperature of the conductor is increased, the r.m.s. velocity vrms is also increased and hence τ is decreased.
Relation between ρ and τ
ρ = \(\frac{m}{ne^2\tau'}\)
where m is the mass of electron, n is number density of electrons and e is the charge on an electron.
