Ohm's law

Ohm’s law says that the current through a device is always directly proportional to the potential difference applied to the device.

$$v(t)=Ri(t)$$ $$i(t)=Gv(t)$$

An alternate statement is given as:

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

where $\sigma$ is the material’s conductivity, $\vec{J}$ is the current density, and $\vec{E}$ is the electric field. Because of the relation of $J$ with the current and $E$ with the potential, this is an equivalent statement as the above.

Devices can obey or disobey the assertion — we say that a material obeys Ohm’s law when the resistivity of the material is independent of the magnitude and direction of the applied electric field.

The graphs below display the i-v characteristic for a) devices that obey Ohm’s law (Ohmic device), b) a lamp filament, c) a diode, and d) a thermistor.

See also

• Power, for an extension of Ohm’s law