The instantaneous voltages at three terminals marked $X, Y$ and $Z$ are given by \[ \begin{aligned} & V_{X}=V_{0} \sin \omega t \\ & V_{Y}=V_{0} \sin \left(\omega t+\frac{2 \pi}{3}\right) \text { and } \\ & V_{Z}=V_{0} \sin \left(\omega t+\frac{4 \pi}{3}\right) . \end{aligned} \] 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) $V_{X Y}^{r m s}=V_{0} \sqrt{\frac{3}{2}}$; (D) independent of the choice of the two terminals

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

JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Alternating Current

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 t + \frac{4 π}{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

Answer: (A), (D)

The potential difference between any two terminals (e.g.,

V_{X Y} = V_{X} - V_{Y}

) can be computed using phasor addition. Since the three voltages are 120° apart, the magnitude of the difference between any two is

3 V_{0}

. The rms value is

\frac{3 V _{0}}{2} = V_{0} \frac{3}{2}

. This value is the same for any pair of terminals, making the reading independent of the choice.

JEE Advanced · 2017 · 21 May 2017 · Paper 2 · One or more correct options