# 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* = *VA*σ/*l*.

*R* = *l*/*A*σ

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** = σ**E**