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? ($T$ = Time period)

$A$ resistance of $20 \Omega$ is connected to an alternating current source of $110 V$. If the frequency of the $A.C.$ source is $50 Hz$,then the time taken by the current to change from its maximum value to the $R.M.S.$ value is

For a domestic $AC$ supply of $220 \ V$ at $50 \ \text{cycles per sec}$, the potential difference between the terminals of a two-pin electric outlet in a room is given by

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

$A$ light bulb is rated at $100\;W$ for a $220\;V$ supply. Find
$(a)$ the resistance of the bulb;
$(b)$ the peak voltage of the source; and
$(c)$ the rms current through the bulb.

What is the $r.m.s.$ value of the current $i = t^2$ for the time interval $0 < t < T$?