Unlike an ohmic conductor, the resistance of an arc decreases as the current increases.

They typically have non-linear current-voltage characteristics, and do not behave as simple ohmic conductors.

The shell is assumed to be an isotropic ohmic conductor; the fields are described by Poisson's equation.

The ionosphere is an ohmic conductor, so some consider that such currents require a driving voltage, which an, as yet unspecified, dynamo mechanism can supply.

In terms of the basic properties of the right-cylindrical current-carrying metallic ohmic conductor, where the charge-carriers are electrons, this expression can be rewritten as :