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?

$A$ direct current of $5\,A$ is superposed on an alternating current $I = 10 \sin \omega t$ flowing through a wire. The effective value of the resulting current will be

An alternating current is given by $I=100 \sin (50 \pi t)$. How many times will the current become zero in one second (in $\times$)?

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

The $r.m.s.$ value of current for a variable current $i = i_1 \cos \omega t + i_2 \sin \omega t$ is:

The voltage of an $ac$ supply varies with time $(t)$ as $V = 120\sin(100\pi t)\cos(100\pi t)$. The maximum voltage and frequency respectively are: