Define the root mean square (rms) value of an alternating current and provide its formula. Also,show the relationship between the rms current and the peak current on a graph of current versus $\omega t$.

(N/A) The root mean square (rms) value of an alternating current is defined as the equivalent steady direct current $(DC)$ which,when flowing through a given resistor,produces the same amount of heat in a given time as the alternating current does over a complete cycle.
The rms current is denoted by $I$ or $I_{rms}$.
The relationship between the rms current $I$ and the peak current $I_{m}$ is given by:
$I = \frac{I_{m}}{\sqrt{2}} \approx 0.707 I_{m}$
Mathematically,it is defined as:
$I_{rms} = \sqrt{\overline{I}^{2}} = \sqrt{\frac{1}{T} \int_{0}^{T} I_{m}^{2} \sin^{2}(\omega t) dt} = \sqrt{\frac{1}{2} I_{m}^{2}} = \frac{I_{m}}{\sqrt{2}}$
Similarly,for voltage:
$V = \frac{V_{m}}{\sqrt{2}} \approx 0.707 V_{m}$
These relations show that $V = IR$ holds for $AC$ circuits using rms values,similar to $DC$ circuits.
The graph of current versus $\omega t$ shows the sinusoidal variation of current with peak value $I_{m}$ and the constant rms value $I$ represented as a horizontal line.