Question

`(i)` Derive an expression for drift velocity of free electrons.
`(ii)` How many drift velocity of electrons in a metallic conductor vary with increase in temperature ? Explain.

Answer 1

`(i)` Expression for drift velocity : When a potential difference is applied across a conductor, an electric field is produced and free electrons are acted upon by an eletric force `(= -Ee)`. Due to this, electrons accelerate and keep colliding with each other and acquire a constant (average) velocity, `v_(d)`
`:. Fe= -Ee=-((V)/(l))e` `:. E=(V)/(l)`
As `a=(-F)/(m)=(-ev)/(lm)` and also `v=u+at` `:. u=0`, `t=tau`(relaxation time)
`v_(d)=-a tau` `v_(d)=(-eV)/(lm)tau`
`(ii)` As temperature is increased no. of collision increases hence `tau` relaxation time decrease but `V_(d)xxtau` so, `V_(d)` decreases.