A series $LR$ circuit is connected to a voltage source with $V(t) = V_0\,\,sin\,\omega t$ . After very large time,current $I(t)$ behaves as $\left( {{t_0} >  > \frac{L}{R}} \right)$ 

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

Find the rms value for the saw-tooth voltage of peak value $V_0$ from $t = 0$ to $t = 2T$ as shown in figure

What is the $r.m.s$. value of an alternating current which when passed through a resistor produces heat which is thrice of that produced by a direct current of $2$ amperes in the same resistor......$amp$

A $110 \,V$ $d.c$. heater is used on an $a.c.$ source, such that the heat produced is same as it produces when connected to $110 \,V$ $dc$ in same time-intervals. What would be the $r.m.s.$ value of the alternating voltage is .......... $V$

If $i = {t^2}$ $0 < t < T$ then $r.m.s$. value of current is