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Statement:β Ohmβs 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. IΞ±V
OrΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β VΞ±I or V= RI
OrΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β 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 Ohmβs Law:
AsΒ drift velocity isΒ given by Vd=eEt/m
ButΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Electric field across the conductor of length l is
E=V/l
ThusΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Vd=e V/ml
Also,Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β I=Anevd
By putting value of vdΒ in the equation of I ,we get
I=Ane(eV/ml)=(Ane2/ml)V
OrΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β V/I=ml/Ane2=R
Where R is a constant for a given conductor. It is known as the resistance of the conductor.
ThusΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β V=RI
ThisΒ is Ohmβs law.
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