MOBILITY OF THE ELECTRON AND CURRENT

Mobility of electron (u_e) is defined as the drift velocity of electron per unit electric field applied.

u_e= drift velocity/electric field= V_d/E

Thus                                 V_d=u_eE

The  SI unit of mobility is m²s^-1V^-1 or ms^-1N^-1C

As  by the relation of the current and drift velocity (already discussed)

I=Anev_d (1)

By putting value of v_d in above equation we get

I=Aneu_eE

OHM’S LAW

Statement:– Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of the conductor,provided physical conditions of the conductors such as temperature,mechanical strain etc. Are kept constant i.e. IαV

Or                                                   VαI or V= RI

Or                                                   V/I=R=a constant

Where R is known as resistance of the conductor . It depends upon the length ,shape and the nature of the material of the conductor. The variation between potential difference (V) and current (I) through a conductor is a straight line.

Deduction of Ohm’s Law:

As drift velocity is given by V_d=eEt/m

But                         Electric field across the conductor of length l is

E=V/l

Thus                              V_d=e V/ml

Also,                              I=Anev_d

By putting value of v_d in the equation of I (equation 1 of relation of the current and drift velocity),we get

I=Ane(eV/ml)=(Ane²/ml)V

Or                        V/I=ml/Ane²=R

Where R is a constant for a given conductor. It is known as the resistance of the conductor.

Thus                                  V=RI

This  is Ohm’s law.