Derive `sigma = (n e^(2) tau)/(m)`
where the symbols have their usual meaning.

Explanation

It is the time interval between two successive collisions of electron with the vibrating atoms of a current carrying conductor.
We know that the relation between electric current (I) and drift velocity `(V_(d))`
`I = n e A V_(d)` -----(1)
Expression for drift velocity in terms of electric field and relaxation time is given by
`V_(d) = (e E tau)/(m)` --------(2)
Substituting (2) in (1) `rArr = I = (n e A e E tau)/(m)`
`rArr I = (n A e^(2) E tau)/(m)`
But `E = (V)/(I)`,
Where `V rarr` Potential across the conductor
`I rarr` length of the conductor
`I = (n A e^(2) V tau)/(ml)`
`(I)/(V) = (n A e^(2) tau)/(ml)`
`(V)/(I) = (ml)/(n A e^(2) tau) rArr R = ((m)/(n A e^(2) tau)) I`
`R = ((m)/(n e^(2) tau))(I)/(A)`
`R = (rho I)/(A)`
Here `rho = (m)/(n e^(2) tau)`
The conductivity of the material
`sigma = (1)/(rho) = (1)/((m)/(n e^(2) tau))`
`sigma = (n e^(2) tau)/(m)`