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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=VX−VY VXY=(VXY)0sin(ωt+θ1) Where (VXY)0=√V20+V20−2V20cos2π3=√3V0 and (VXY)rms=(VXY)0√2√32V0 ∴ option A is the correct option , now the potential diffrence between Y and Z is VYZ=VY−VZ VYZ=(VYZ)0sin(ωt+θ2) Where (VYZ)0=√V20+V20−2V20cos2π3=√3V0 and (VYZ)rms=(VYZ)0√2√32V0 ∴ option D is the correct answer

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