GATE 2024 EE – Question 50
In the circuit shown, $Z_1=50\angle-90^\circ\ \Omega$ and $Z_2=200\angle-30^\circ\ \Omega$. It is supplied by a three phase 400 V source with the phase sequence being R-Y-B. Assume the watt meters $W_1$ and $W_2$ to be ideal. The magnitude of the difference between the readings of $W_1$ and $W_2$ in watts is ___________ (rounded off to 2 decimal places).
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Correct answer: 689.36 to 696.28
Explanation
Take $V_{RY}=400\angle0^\circ$; for R-Y-B sequence $V_{YB}=400\angle-120^\circ$ and $V_{RB}=400\angle-60^\circ$. $Z_1$ is across R–B and $Z_2$ across R–Y: $I_1=\dfrac{V_{RB}}{Z_1}=8\angle30^\circ$ A and $I_2=\dfrac{V_{RY}}{Z_2}=2\angle30^\circ$ A. The line currents are $I_R=I_1+I_2=10\angle30^\circ$ and $I_Y=-I_2=2\angle-150^\circ$. $W_1$ (current in R, potential across R–B): $400\times10\cos(-60^\circ-30^\circ)=0$. $W_2$ (current in Y, potential across Y–B): $400\times2\cos(-120^\circ+150^\circ)=800\cos30^\circ=692.82$ W. The difference is 692.82 W.