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GATE 2020 EC – Question 38

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 2 marks · Multiple choice

The current $I$ in the given network is

Diagram for GATE 2020 EC question 38
  1. 0 A.
  2. $2.38\angle-96.37^\circ$ A.
  3. $2.38\angle143.63^\circ$ A.
  4. $2.38\angle-23.63^\circ$ A.

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Correct answer: (C) $2.38\angle143.63^\circ$ A.

Explanation

Take the common node of the two sources and the middle of the two $Z$ impedances as the reference, which are joined by the wire carrying $I$. The top and bottom nodes are then at $V_T=120\angle-90^\circ=-j120$ V and $V_B=120\angle-30^\circ=103.9-j60$ V. The current in the wire is $I=-\frac{V_T+V_B}{Z}=-\frac{103.9-j180}{80-j35}=-\frac{207.8\angle-60^\circ}{87.3\angle-23.63^\circ}=-2.38\angle-36.37^\circ=2.38\angle143.63^\circ$ A.