A current density J and an electric field E are established in an object that has a potential difference ΔV across it. In some materials the current density is directly proportional to the electric field - these are known as ohmic materials.

Ohm's Law: J = σE

where σ is the conductivity of the material, a measure of how easily charges move through it.

Resistivity is the inverse of conductivity:   ρ

=

1 σ

Combine this with:

J

=

I A

and, for a uniform field,   E

=

ΔV l

where l is the length of the conductor.

I A

=

ΔV ρ l

ΔV

= I

(

ρ l A

)

This is another form of Ohm's Law: ΔV = IR

where R, the resistance of the conductor, is given by   R

=

ρ l A