Question

Derivation of ohm's law

Answer 1

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

E=V/l

Thus Vd=e V/ml

Also, I=Anevd

By putting value of vd 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.

Answer 2

$\textbf{Answer is in Attachment !}$