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GATE 2022 EE – Question 21

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 1 mark · Multiple choice

In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of $100\sqrt3$ V with phase sequence $ABC$. The star connected load has $Z_A=10\ \Omega$ and $Z_B=20\angle60^\circ\ \Omega$. The value of $Z_C$ in $\Omega$, for which the voltage difference across the nodes $n$ and $n'$ is zero, is

Diagram for GATE 2022 EE question 21
  1. $20\angle-30^\circ$
  2. $20\angle30^\circ$
  3. $20\angle-60^\circ$
  4. $20\angle60^\circ$

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Show answer and explanation

Correct answer: (C) $20\angle-60^\circ$

Explanation

The phase voltages are $E_A=100\angle0^\circ$, $E_B=100\angle-120^\circ$, $E_C=100\angle120^\circ$. The neutral shift is zero when $\frac{E_A}{Z_A}+\frac{E_B}{Z_B}+\frac{E_C}{Z_C}=0$. The first two currents are $10\angle0^\circ$ and $5\angle-180^\circ=-5$, so $\frac{E_C}{Z_C}=-5$ and $Z_C=\frac{100\angle120^\circ}{5\angle180^\circ}=20\angle-60^\circ$.