Voltage and current in an $ac$ circuit are given by $V = 5\sin(100\pi t - \frac{\pi}{6})$ and $I = 4\sin(100\pi t + \frac{\pi}{6})$. Which of the following statements is correct?

The $r.m.s.$ voltage of the waveform shown is:

The average value of alternating current over a complete cycle 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

An electric lamp is connected to a $220 V, 50 Hz$ supply. The peak value of the voltage is......$V$.

$A$ resistance of $20 \, \Omega$ is connected to a source of an alternating potential $V = 220 \sin(100 \pi t)$. The time taken by the current to change from its peak value to its r.m.s. value is: