Ohm’s law and its derivation
MOBILITY OF THE ELECTRON AND CURRENT
Mobility of electron (ue) is defined as the drift velocity of electron per unit electric field applied.
ue= drift velocity/electric field= Vd/E
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)
By putting value of vd in above equation we get
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 Vd=eEt/m
But Electric field across the conductor of length l is
Thus Vd=e V/ml
By putting value of vd in the equation of I (equation 1 of relation of the current and drift velocity),we get
Where R is a constant for a given conductor. It is known as the resistance of the conductor.
This is Ohm’s law.