The instantaneous voltages at three terminals marked $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ are given by

$V_x=V_0 \sin \omega t$ $V_y=V_0 \sin \left(\omega t+\frac{2 \pi}{3}\right) \text { and }$ $V_z=V_0 \sin \left(\omega t+\frac{4 \pi}{3}\right)$

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points $\mathrm{X}$ and $\mathrm{Y}$ and then between $\mathrm{Y}$ and $\mathrm{Z}$. The reading(s) of the voltmeter will be

$[A]$ $\mathrm{V}_{\mathrm{XY}}^{\mathrm{mms}}=\mathrm{V}_0 \sqrt{\frac{3}{2}}$

$[B]$ $\mathrm{V}_{\mathrm{YZ}}^{\mathrm{mms}}=\mathrm{V}_0 \sqrt{\frac{1}{2}}$

$[C]$ $\mathrm{V}_{\mathrm{XY}}^{\mathrm{mms}}=\mathrm{V}_0$

$[D]$ independent of the choice of the two terminals

When a $DC$ voltage of $200\, V$ is applied to a coil of self inductance $\frac{{2\sqrt 3 }}{\pi }\,H$, a current of $1\, A$ flows through it. But by replacing $DC$ source with $AC$ source of $200\, V$, the current in the coil is reduced to $0.5\, A$. Then, the frequency of $AC$ supply is......$Hz$

The charge in an $LC$ circuit with negligible resistance oscillates as given by equation $\frac{{{d^2}q}}{{d{t^2}}} + 16{\pi ^2}q = 0$. If the charge is maxiumum equal to $24\,\mu C$ at $t = 0$, find the charge at $t = \frac{1}{{12}}\,s$............$\,\mu C$

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) $\frac{{{x_0}}}{{(2\sqrt 2 )}}$

What will be $r.m.s.$ value of given $A.C.$ over one cycle.

What are $A.C.$ signals ?