The alternating current is given by $i = \left\{\sqrt{42} \sin \left(\frac{2 \pi}{T} t\right) + 10\right\} \text{ A}$. The $r.m.s.$ value of this current is $\text{A}$.

The frequency of an alternating voltage is $50 \ Hz$. The time taken for the instantaneous voltage to increase from zero to half of its peak voltage is:

An electric bulb rated as $100 \ W-220 \ V$ is connected to an $ac$ source of $rms$ voltage $220 \ V$. The peak value of current through the bulb is: (in $A$)

The sinusoidal potential difference $V_1$ shown in the figure is applied across a resistor $R$,producing heat at a rate $W$. What is the rate of heat dissipation when the square wave potential difference $V_2$ as shown in the figure is applied across the same resistor?

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In what time will the e.m.f. reach half its maximum value, if $e$ starts from zero? (Given: $\sin 30^{\circ} = 0.5$)

What is the average value of the $AC$ voltage over a complete cycle?