Prove that power dissipated in an ideal resistor connected to an $\mathrm{AC}$ source is ${{\mathrm{V}}_{\mathrm{eff}}}^2/\mathrm{R}$.

Define peak value of an alternating current, average value for half-cycle, root-mean-square value of $\mathrm{AC}$ and obtain the relation.

${\mathrm{I}}_{\mathrm{rms}}=\frac{{\mathrm{I}}_0}{\sqrt{2}}$