Discussion Forum



1)

The instantaneous voltage at three terminals marked X, Y and Z are given by VX= V0 sinωt.

$V_{Y}=V_{0}\sin(\omega t+\frac{2\pi}{3}) and$

$V_{Z}=V_{0}\sin(\omega t+\frac{4\pi}{3})$

 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


A) $V_{YZ}^{rms}=V_{0}\sqrt{\frac{1}{2}}$

B) $V_{XY}^{rms}=V_{0}\sqrt{\frac{3}{2}}$

C) independent of the choice of the two terminals

D) $V_{XY}^{rms}=V_{0}$

Answer:

Option B,C

Explanation:

$V_{XY}=V_{0}\sin(\omega t+\frac{2\pi}{3})-V_{0}\sin\omega t$

  = $V_{0}\sin(\omega t+\frac{2\pi}{3})+V_{0}\sin(\omega t+\pi)$

$\Rightarrow$   $\phi =\pi -\frac{2\pi}{3}=\frac{\pi}{3}$

$\Rightarrow$   $V_{0}^{'}= 2V_{0}\cos(\frac{\pi}{6})$

            = $\sqrt{3}V_{0}$

$\Rightarrow$    $V_{XY}=\sqrt{3}V_{0}\sin (\omega t+\phi)$

$(V_{XY})_{rms}= (V_{YZ})_{rms}=\sqrt{3}\frac{V_{0}}{\sqrt{2}}$