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Ohm's law states that resistance and current are proportional to voltage by the equation

$ V = IR $

by dividing by area, this becomes

$ \vec{\mathbf{J}} = \sigma \vec{\mathbf{E}} $

where J is current density, σ is conductivity, and E is the electric field strength in the wire. For AC circuits, this becomes

$ V_{rms} = I_{rms} \cdot Z $

with Z representing impedance. This is a more general form of Ohm's law.

Ohm's law is not always followed. All materials will experience an electrical breakdown (a spark) given a high enough voltage, and some materials, such as diodes, do not follow Ohm's law even at low voltages.