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← JEE Advanced 2017 · Paper 2
PhysicsMultiple correct+4 / -2Question 9 of 54

JEE Advanced 2017 · Paper 2, Physics question 9

The instantaneous voltages at three terminals marked XX, YY and ZZ are given by

VX=V0sin⁡ωt,VY=V0sin⁡(ωt+2π3) and VZ=V0sin⁡(ωt+4π3).V_X = V_0\sin\omega t,\quad 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).

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points XX and YY and then between YY and ZZ. The reading(s) of the voltmeter will be

Choose one or more options
Answer and worked solution

Official answer: A, D

Line voltages. Two sinusoids of amplitude V0V_0 that are 120∘120^\circ apart differ by a sinusoid of amplitude 2V0sin⁡60∘=3V02V_0\sin60^\circ=\sqrt3V_0.

rms value.
Vrms=3V02=V032.V^{rms}=\frac{\sqrt3V_0}{\sqrt2}=V_0\sqrt{\tfrac32}.
This is the same for every pair of terminals.

(A), (D)