Question

The instantaneous voltages at three terminals marked $X , Y$ and $Z$ are given by $V _{ x }= V _{0} \sin \omega t$ $V _{ y }= V _{0} \sin \left(\omega t +\frac{2 \pi}{3}\right)$ 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 $X$ and $Y$ and then between $Y$ and $Z$. The reading(s) of the voltmeter will be

• A. $V^{rms}_{xy} = V_{0}\sqrt{\frac{3}{2}}$
• B. $V^{rms}_{xy} = V_{0}\sqrt{\frac{1}{2}}$
• C. $V^{rms}_{xy} = V_{0}$
• D. independent of the choice of the two terminals

Answer 1

Answer: (D)

independent of the choice of the two terminals

Answer 2

$V _{ XYO }= V _{ Y 2 O }= V _{ ZXO }=\sqrt{3} V _{0}$
$V _{ XX }^{ ms }= V _{ YZ }^{ rms }=\sqrt{\frac{3}{2}} V _{0}$