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 alternating current of frequency $50 \,Hz$ has a peak value of $14.14 \,A$. The time taken by the alternating current to reach from zero to its maximum value and the root mean square (r.m.s.) value of the current are respectively:

The average value of the potential difference $V$ shown in the figure is:

Match the following:
Currents $r.m.s.$ values
$(1) x_0 \sin \omega t$ $(i) x_0$
$(2) x_0 \sin \omega t \cos \omega t$ $(ii) \frac{x_0}{\sqrt{2}}$
$(3) x_0 \sin \omega t + x_0 \cos \omega t$ $(iii) \frac{x_0}{2\sqrt{2}}$

An $ac$ generator produces an output voltage $E = 170 \sin(377t) \text{ volts}$,where $t$ is in seconds. The frequency of the $ac$ voltage is......$Hz$.

An alternating current of $rms$ value $10 \, A$ is passed through a $12 \, \Omega$ resistor. The maximum potential difference across the resistor is