Find the time required for $50\,Hz$ alternating current to change its value from zero to maximum value.

Match the following current $\text{r.m.s.}$ values:

$(A) \ x_0 \sin \omega t$	$(i) \ x_0$
$(B) \ x_0 \sin \omega t \cos \omega t$	$(ii) \ \frac{x_0}{\sqrt{2}}$
$(C) \ x_0 \sin \omega t + x_0 \cos \omega t$	$(iii) \ \frac{x_0}{2 \sqrt{2}}$

The r.m.s. voltage of domestic electricity supply is $220 \ V$. Electrical appliances should be designed to withstand an instantaneous voltage of......$V$.

An electric lamp is connected to a $220 V, 50 Hz$ supply. The peak value of the voltage is......$V$.

$A$ resistance of $20 \Omega$ is connected to a source of an alternating potential $V = 200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value,then $t$ is (in seconds).

The heat produced in a resistor by an $AC$ current is three times the heat produced by a $2 \, A$ $DC$ current. What is the $rms$ value of the $AC$ current in $A$?