Ohm's Law

Ohm's Law is the linear proportionality between current and voltage that occurs for most conductors of electricity. A graph of voltage against current is a straight line. The gradient is the resistance.

The most well known form of Ohm's law is V=IR, where V is the voltage, I is the current and R is the resistance. However there is another form of Ohm's law which often used by physicists that operates on a microscopic level, relating the current density J to the conductivity σ and the electric field, E.

To see how consider, the volume of material with faces of area A a distance I apart. With an e.m.f. V across the faces of the material:

the current is proportional to the voltage V
the current is proportional to the surface area A
and the current is inversely proportional to the distance I.
The current is therefore,

I = VAσ/I.

R = I/Aσ

The proportionality constant σ is the conductivity of the material.

V/I = |E|, and J = I/A in the direction of E so in general we have the constitutive relation.

J = σE

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