An alternating current is given by the equation $i = i_{1} \sin \omega t + i_{2} \cos \omega t$. The rms current will be

  • A
    $\frac{1}{\sqrt{2}}(i_{1}^{2} + i_{2}^{2})^{1/2}$
  • B
    $\frac{1}{\sqrt{2}}(i_{1} + i_{2})^{2}$
  • C
    $\frac{1}{2}(i_{1}^{2} + i_{2}^{2})^{1/2}$
  • D
    $\frac{1}{\sqrt{2}}(i_{1} + i_{2})$

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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

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