Question

For a fixed conductor at a fixed temperature, which of the following is not the mathematical statement of Ohm’s law?( V = potential difference, I = current, E = electric field, J = current density, = resistivity, = conductivity, l = length of conductor, A = area of conductor) *

(a) V ∝ I

(b) E = J ρ

(c) J = σ E

(d) R = ρ l/A

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Answer 1

Answer:

Let I current flow through a conductor when applied potential difference V volt. then, from ohm’s law,

I=

R

V

But R=ρ

A

L

Therefore,

I=

ρ

A

L

V

⟹

A

I

=

ρL

V

but,

A

I

=J,

L

V

=E

Hence, J=σE

⟹σ=

E

J