GATE 2023 EE – Question 64
A balanced delta connected load consisting of the series connection of one resistor ($R=15\ \Omega$) and a capacitor ($C=212.21\ \mu$F) in each phase is connected to three-phase, 50 Hz, 415 V supply terminals through a line having an inductance of $L=31.83$ mH per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals $V_{AB}$ in Volts is _____________ (Round off to the nearest integer).
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Correct answer: 415
Explanation
At 50 Hz, $X_C=\dfrac1{2\pi\times50\times212.21\times10^{-6}}=15\ \Omega$ and $X_L=2\pi\times50\times31.83\times10^{-3}=10\ \Omega$. Each delta phase has $15-j15\ \Omega$, equivalent to a star impedance of $5-j5\ \Omega$. Per-phase circuit: $I=\dfrac{415/\sqrt3}{j10+5-j5}=\dfrac{239.6}{5+j5}$, so $|I|=33.9$ A. The load phase voltage is $|I|\times|5-j5|=33.9\times7.07=239.6$ V, the same as the source phase voltage (the line inductance exactly compensates the capacitive reactance). So $V_{AB}=\sqrt3\times239.6=415$ V.