Figure shows a resistor connected to an ac voltage.

Here consider a source which produces sinusoidally varying potential difference across its

terminals. Such type of potential difference is called ac voltage.

$\therefore$ ac voltage $\mathrm{V}=\mathrm{V}_{\mathrm{m}} sin\omega t$$…..(1)$

where $\mathrm{V}_{\mathrm{m}}$ is the amplitude of the oscillating potential difference. Means maximum voltage and $\omega$

is its angular frequency.

From equation $(1)$, $\mathrm{V}=\mathrm{IR}$

where $\mathrm{I}$ can be found by applying Kirchhoff's loop rule,

$\therefore \mathrm{IR}=\mathrm{V}_{\mathrm{m}} sin\omega t$

$\therefore \mathrm{I}=\frac{\mathrm{V}_{\mathrm{m}}}{\mathrm{R}} \sin \omega t$

but $\frac{\mathrm{V}_{\mathrm{m}}}{\mathrm{R}}=\mathrm{I}_{\mathrm{m}}$

$\therefore \mathrm{I}=\mathrm{I}_{\mathrm{m}} \sin \omega t$ $….(2)$

where the current amplitude is,

$\mathrm{I}_{\mathrm{m}}=\frac{\mathrm{V}_{\mathrm{m}}}{\mathrm{R}}$ is just a Ohm's law.

This relation works equally for both ac and dc voltages or current (signal).

The voltage across a pure resistor and current through it are plotted as a function of time is shown in below graph.