devarshi-dt-logo

Question:

The instantaneous voltages at three terminals marked X, Y and Z are given by: VX=V0sinωt, VY=V0sin(ωt+2π/3), and VZ=V0sin(ωt+4π/3). An ideal voltmeter is configured to read the rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z. What will be the reading (S) of the voltmeter?

VrmsYZ=V0√1/2

VrmsXY=V0√3/2

VrmsXY=V0

Independent of the choice of the two terminals

Solution:

Vxy=√V0² + V0² + 2V0V0cos120°
Vxy=V0
As we know the rms value is a factor of the square root of the normal value. So,
Vrmsxy=V0√2
Hence A is correct.
All the three components will cancel each other as the resultant of two components will be the opposite of the third component. Hence it will be canceled.
So for both combinations, it will be independent.
Hence D is also correct.