The instantaneous voltages at three terminals marked X, Y and Z are given by
$V_{X} = V_{0} sin ω t$
$V_{Y} = V_{0} sin (ω t + \frac{2 π}{3})$ and
$V_{Z} = V_{0} sin (ω_{0} + \frac{4 π}{3})$
An ideal voltmeter is configured to read rms of the value of potential difference between its terminals. It is connected between points points X and Y and then between Y and Z. The reading (S) of the voltmeter will be

V_{Y Z}^{r m s} = V_{0} \sqrt{\frac{1}{2}}

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V_{X Y}^{r m s} = V_{0} \sqrt{\frac{3}{2}}

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V_{X Y}^{r m s} = V_{0}

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Independent of the choice of the two terminals

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Solution

The correct options are
B $V_{Y Z}^{r m s} = V_{0} \sqrt{\frac{1}{2}}$
D Independent of the choice of the two terminals
$V_{x y} = \sqrt{V_{0}^{2} + V_{0}^{2} + 2 V_{0} V_{0} c o s 120^{0}}$
$V_{x y} = V_{0}$
As we know the rms value is a factor of the square root of the normal value. So,
$V_{x y}^{r m s} = \frac{V_{0}}{\sqrt{2}}$
Hence A is correct.
All the three component will be cancelled each other as the resultant of two component will be the opposite of the third component. Hence it will be get cancelled.
So for the both combination, it will be independent.
Hence D is also correct.

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