# derive ohm's law in microscopic form​

Physics

## Question

derive ohm's law in microscopic form​

• ### 1. User Answers roshankr1000

Let us consider a conductor of length L having cross-sectional area A. Let i is the current passing through through the conductor and R is the resistance of the conductor and V is the potential difference applied across the two ends of the conductor then by ohm's law :-

V=iR ........(1)

Since the resistance of a conductor with resistivity r, length L and area A is given by :-

R=rL/A

Putting above value of R in equation (1) :-

V=irL/A .........(2)

If E is the electric field intensity across the ends of conductor and V is the potential difference then the relation between field and potential difference is

V=EL .........(3)

Comparing equation (2) and equation (3) :-

EL=irL/A

E=ir/A

E=(i/A)r .........(4)

Since by definition of current density J :-

J=i/A

Putting this value in equation (4) :-

E=Jr

Since r is resistivity and conductivity c is the the reciprocal of resistivity i.e

c=1/r

=> r=1/c

Hence;

E=J/c

=> J=cE .........(5)

Equation (5) is the Microscopic Form of Ohm's Law in terms of conductivity, electric field intensity and current density.

• ### 2. User Answers Anonym

Explanation:

Ohm's Law :-

It states that , on a constant temperature , the current  I , flowing through the electric circuit , is directly proportional to the potential difference V , across its ends.

V ∝ I

I ∝ V

V/ I = R , constant of proportionality

R = Resistance [ opposes flow of current ]

V  = IR

R = V/I

I = V / R