The mean and $rms$ value of an alternating voltage for a half cycle,as shown in the figure,are respectively:

An $AC$ source has a voltage of $220V$ and a frequency of $50\,Hz$. How much time (in $sec$) does it take for the voltage to reach zero from its maximum value?

Match the following:

Currents	$r.m.s.$ values
$(A) \ x_0 \sin \omega t$	$(i) \ x_0$
$(B) \ x_0 \sin \omega t \cos \omega t$	$(ii) \ \frac{x_0}{\sqrt{2}}$
$(C) \ x_0 \sin \omega t + x_0 \cos \omega t$	$(iii) \ \frac{x_0}{2\sqrt{2}}$

$A$ direct current of $5\,A$ is superposed on an alternating current $I = 10 \sin \omega t$ flowing through a wire. The effective value of the resulting current will be

The average value of alternating current $I = I_0 \sin \omega t$ in the time interval $[0, \frac{\pi}{\omega}]$ is:

An alternating e.m.f. is given as $e = e_0 \sin \omega t$. In what time will the e.m.f. have half its maximum value if $e$ starts from zero?
$(T = \text{time period}, \sin 30^{\circ} = \cos 60^{\circ} = 0.5)$