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
- $V^{rms}_{xy} = V_{0}\sqrt{\frac{3}{2}}$
- $V^{rms}_{xy} = V_{0}\sqrt{\frac{1}{2}}$
- $V^{rms}_{xy} = V_{0}$
- independent of the choice of the two terminals
The Correct Option is D
Solution and Explanation
$V _{ XX }^{ ms }= V _{ YZ }^{ rms }=\sqrt{\frac{3}{2}} V _{0}$
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Concepts Used:
AC Voltage
When voltage changes its direction after every half cycle is known as alternating voltage. The current flows in the circuit at that time are known as alternating current. The alternating current(AC) follows the sine function which changes its polarity concerning time. Most of the electrical devices are operating on the ac voltage.
