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

$${V_x} = {V_0}\,\sin \,\omega t,$$

$${V_Y} = {V_0}\,\sin $$ $$\left( {\omega t + {{2\pi } \over 3}} \right)$$

and $$Vz = {V_0}\sin \left( {\omega t + {{4\pi } \over 3}} \right)$$

An ideal voltmeter is configured to read $$rms$$ 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

In the circuit shown, $$L = 1\,\mu H,C = 1\,\mu F\,$$ and $$R = 1\,k\Omega .$$ They are connected in series with an a.c. source $$V = {V_0}\sin \omega t$$ as shown.

Which of the following options is/are correct?

At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I₀ cos ($$\omega$$t), with I₀ = 1 A and $$\omega$$ = 500 rad s^-1 starts flowing in it with the initial direction shown in the figure. At $$t = {{7\pi } \over {6\omega }}$$, the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 $$\mu$$F, R = 10 $$\Omega$$ and the battery is ideal with emf of 50 V, identify the correct statement(s).

In the given circuit, the AC source has $$\omega$$ = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)