The $r.m.s.$ voltage of the waveform shown is......$V$

An alternating voltage is given by $E = 100 \sin \left(\omega t + \frac{\pi}{6}\right) \text{ V}$. The voltage will be maximum for the first time when $t$ is $(T = \text{periodic time})$:

Find the effective value of current $i = 2\sin(100\pi t) + 2\cos(100\pi t + 30^{\circ})$.

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:

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.

An alternating e.m.f. is given as $e = e_0 \sin \omega t$. In what time will the e.m.f. have half its maximum value if $e$ starts from zero?
$(T = \text{time period}, \sin 30^{\circ} = \cos 60^{\circ} = 0.5)$