In a circuit,the value of the alternating current is measured by a hot wire ammeter as $10 \ A$. Its peak value will be: (in $A$)

The frequency of $AC$ mains in India is ....... $Hz$.

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?

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

In a circuit,current varies with time as $i = 2\sqrt{t}$. The root mean square value of current for the interval $t = 2\,s$ to $t = 4\,s$ is:

The instantaneous voltages at three terminals marked $X, Y$ and $Z$ are given by
$V_x = V_0 \sin \omega t$
$V_y = V_0 \sin \left(\omega t + \frac{2 \pi}{3}\right)$
$V_z = V_0 \sin \left(\omega t + \frac{4 \pi}{3}\right)$
An ideal voltmeter is configured to read the $rms$ value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z$. The reading$(s)$ of the voltmeter will be:
$[A]$ $V_{XY}^{rms} = V_0 \sqrt{\frac{3}{2}}$
$[B]$ $V_{YZ}^{rms} = V_0 \sqrt{\frac{1}{2}}$
$[C]$ $V_{XY}^{rms} = V_0$
$[D]$ independent of the choice of the two terminals