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GATE 2015 EE (EE2) – Question 54

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 · 2 marks · Multiple choice

The circuit has $V_1=100\angle0^\circ$ V, $V_2=100\angle-120^\circ$ V, $V_3=100\angle120^\circ$ V. Find phasor current i in amperes.

Diagram for GATE 2015 EE (EE2) question 54
  1. $173.2\angle-60^\circ$
  2. $173.2\angle120^\circ$
  3. $100\angle-60^\circ$
  4. $100\angle120^\circ$

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Correct answer: (A) $173.2\angle-60^\circ$

Explanation

Use the bottom source V3 to fix the common terminal voltage. The upper branch current is (V1−V3)/(−j) and the middle current is (V2−V3)/j.

KCL gives the indicated bottom current as the negative of their sum: i=−j(V1−V2). Since V1−V2=150+j86.6025, i=86.6025−j150.

Its magnitude and angle are **173.205 A and −60°, A**.

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