Give definition and formula of root mean square plot graph of current versus $\omega t$.

Root mean square of any physical quantity is called root mean square. In short rms or it is also called effective quantity.

rms current is denoted by $I$ or $\mathrm{I}_{\mathrm{rms}}$. The graph of $I$ versus $\omega t$ is given below.

The rms current $I$ is related to peak current $I_{m}$ by

$\mathrm{I}=\frac{\mathrm{I}_{\mathrm{m}}}{\sqrt{2}}=0.707 \mathrm{I}_{\mathrm{m}}$

$\mathrm{I}_{\mathrm{rms}} =\sqrt{\overline{\mathrm{I}}^{2}}$

$=\sqrt{\frac{1}{2} \mathrm{I}_{\mathrm{m}}^{2}}$

$=\frac{\mathrm{I}_{\mathrm{m}}}{\sqrt{2}}=0.707 \mathrm{I}_{\mathrm{m}}$

Formula of rms for average power,

$\mathrm{P}=\bar{p}=\frac{1}{2} \mathrm{I}_{\mathrm{m}}^{2} \mathrm{R}=\mathrm{I}_{\mathrm{rms}}^{2} \mathrm{R}\left[\because \frac{1}{2} \mathrm{I}_{m}^{2}=\mathrm{I}_{\mathrm{rms}}^{2}\right]$

and rms value for voltage,

$\mathrm{V}=\frac{\mathrm{V}_{\mathrm{m}}}{\sqrt{2}}=0.707 \mathrm{~V}_{\mathrm{m}}$

Now $V_{m}=I_{m} R$ or $\frac{V_{m}}{\sqrt{2}}=\frac{I_{m}}{\sqrt{2}} R$ or $V=I R$. These equations shows the relation between $ac$ voltage and $ac$ current.

It is similar to that in the $dc$ case.