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 l 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 l.

The current is therefore,

I = VAσ/l.

R = l/Aσ

The proportionality constant σ is the conductivity of the material.

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

J = σE