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Question

The instantaneous voltages at three terminals marked X, Y and Z are given by

VX=V0sinωt

VY=V0sin(ωt+2π3) and

VZ=V0sin(ω0+4π3)

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


A
(VXY)rms=Vo32
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B
(VYZ)rms=Vo12
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C

(VXY)rms=Vo

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D

Independent of the choice of the two terminals

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Solution

The correct option is D

Independent of the choice of the two terminals




The potential diffrence between X and Y is

VXY=VXVY
VXY=(VXY)0sin(ωt+θ1)
Where (VXY)0=V20+V202V20cos2π3=3V0
and (VXY)rms=(VXY)0232V0
option A is the correct option ,
now the potential diffrence between Y and Z is

VYZ=VYVZ
VYZ=(VYZ)0sin(ωt+θ2)
Where (VYZ)0=V20+V202V20cos2π3=3V0
and (VYZ)rms=(VYZ)0232V0
option D is the correct answer


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