Relation between Current and Drift velocity :-

Suppose a potential difference V is electric field E is applied across a conductor of length I and uniform area of cross- section A. the electric field E is set up inside the conductor is given by  .

Under the influence of electric field E, the free electrons begin to drift in the opposite direction E with an average drift velocity v_d.

Let the number of electrons per unit volume or electrons density = n

Charge on an electron = e

Number of electrons in length I of the conductor,

= n* volume of the conductor

= n A L

Total charge contained in length I of the conductor,

Q = en A L

All the electrons which enters the conductor at the right end will pass through the conductor at the left end in time,

this equation relates the current I with the drift velocity ν_d. the current density I

 Ohm’s law on the basis of the theory of electron drift :- if m is mass of an electron and τ is the relaxation time, then drift velocity

Therefore, current 

At a fixed temp., the quantities m, l, n, e, τ, and A, all have constant value for a given conductor. Therefore,

This proves ohm’s law for a conductor and here is the resistance of the conductor.