Electromagnetic Induction and Alternating Current 6 Question 9

####9. The instantaneous voltages at three terminals marked X,Y and Z are given by VX=V0sinωt,

VY=V0sin(ωt+2π3) and VZ=V0sin(ωt+4π3).

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

(2017 Adv.)

(a) (VYZ)rms=V012

(b) (VXY)rms=V032

(c) independent of the choice of the two terminals

(d) (VXY)rms=V0

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Answer:

Correct Answer: 9. (b, c)

Solution:

  1. VXY=V0sinωt+2π3V0sinωt

=V0sinωt+2π3+V0sin(ωt+π)

φ=π2π3=π3

V0=2V0cosπ6=3V0

VXY=3V0sin(ωt+φ)

(VXY)rms=(VYZ)rms=32V0



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