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GATE 2021 EE – Question 46

Power Systems · Symmetrical components, Symmetrical and unsymmetrical fault analysis · 2 marks · Multiple choice

Suppose $I_A$, $I_B$ and $I_C$ are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current $I_{B0}=0.1\angle0^\circ$ p.u. If phase-A current $I_A=1.1\angle0^\circ$ p.u and phase-C current $I_C=(1\angle120^\circ+0.1)$ p.u, then $I_B$ is in p.u is

  1. $1\angle240^\circ-0.1\angle0^\circ$
  2. $1.1\angle240^\circ-0.1\angle0^\circ$
  3. $1.1\angle-120^\circ+0.1\angle0^\circ$
  4. $1\angle-120^\circ+0.1\angle0^\circ$

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Correct answer: (D) $1\angle-120^\circ+0.1\angle0^\circ$

Explanation

The zero-sequence component is the same for all phases, $I_0=\frac{I_A+I_B+I_C}{3}=0.1$, so $I_B=0.3-I_A-I_C=0.3-1.1-1\angle120^\circ-0.1=-0.9-(-0.5+j0.866)=-0.4-j0.866$. Option D is $1\angle-120^\circ+0.1=-0.5-j0.866+0.1=-0.4-j0.866$.