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GATE 2014 EC (EC3) – Question 41

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

Find node voltage V₂ in the circuit shown.

Diagram for GATE 2014 EC (EC3) question 41
  1. 22 + j2 V
  2. 2 + j22 V
  3. 22 − j2 V
  4. 2 − j22 V

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Show answer and explanation

Correct answer: (D) 2 − j22 V

Explanation

The voltage source imposes V1−V2=10. The capacitor admittance is j/3 and the right shunt admittance is(1−j)/6. Supernode KCL gives(j/3)V1+[(1−j)/6]V2=4; the4Ωbranch is internal. Substitute V1=V2+10 to obtain(1+j)V2=24−20j. Hence **V2=2−j22V,D**.