A potential difference can drive current through a component. Resistance describes how strongly that component opposes current in its operating regime.

For an ohmic component,

$$\boxed{V=IR},$$

where $V$ is the voltage across the component, $I$ is the current through it, and $R$ is its resistance.

The SI unit is the ohm:

$$1,\Omega=1,\mathrm{V/A}.$$

Equivalently,

$$R=\frac{V}{I}$$

when the component obeys a linear voltage-current relation through the origin.

Ohm's law is a constitutive model

Ohm's law is not a universal law applying to every electrical device. It describes components or materials whose current is approximately proportional to applied voltage under the specified operating conditions.

On a graph of $V$ versus $I$, an ideal ohmic resistor gives a straight line whose slope is

$$\boxed{R=\frac{\Delta V}{\Delta I}}.$$

A diode, filament lamp over a wide temperature range, gas discharge, and many semiconductor devices have nonlinear current-voltage relationships and therefore cannot be represented by one constant $R$ over all conditions.

Worked example

A resistor has

$$R=15,\Omega$$

and a voltage magnitude

$$V=6.0,\mathrm V$$

across it. Its current magnitude is

$$I=\frac{V}{R} =\frac{6.0}{15} =\boxed{0.40,\mathrm A}.$$

If the voltage reverses polarity while the resistance remains unchanged, the current reverses direction as well.

Resistance versus resistivity

Resistance characterizes a particular component. It can change if the component's dimensions, material state, or temperature change.

The material-level quantity that relates local electric field to local current density is resistivity. For a uniform wire, resistivity and geometry combine to determine its resistance. That relation is a separate bridge between the local material description and the lumped circuit model.

Ohm's law therefore supplies the voltage-current relation needed for circuit analysis, while microscopic conduction models explain when and why a material produces an approximately constant resistance.