In an $a.c.$ circuit,the instantaneous current and $emf$ are represented as $I = I_0 \sin(\omega t - \pi / 6)$ and $E = E_0 \sin(\omega t + \pi / 3)$ respectively. The voltage leads the current by

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)

The ratio of the peak value to the root mean square (r.m.s.) value of an alternating current is:

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?

In an $ac$ circuit,the instantaneous voltage $e(t)$ and current $i(t)$ are given by $e(t) = 5[\cos \omega t + \sqrt{3} \sin \omega t] \ V$ and $i(t) = 5[\sin(\omega t + \frac{\pi}{4})] \ A$. Determine the phase relationship between voltage and current.

Both alternating current and direct current are measured in amperes. But how is the ampere defined for an alternating current?