The GATE Grind

GATE 2025 IN – Question 25

Electrical Circuits and Machines · AC circuits and resonance · 1 mark · Multiple choice

Three admittances $Y_a=-j0.2$ S, $Y_b=0.3$ S, and $Y_c=j0.4$ S are connected in parallel across $V_s=10\angle45^\circ$ V. Their currents are $I_a,I_b,I_c$ and the total current is $I_s$. Let $I=I_b+I_c$. The phase relation between $I$ and $I_s$ is

  1. $I$ leads $I_s$ by $19.44^\circ$
  2. $I$ lags $I_s$ by $19.44^\circ$
  3. $I$ leads $I_s$ by $33.69^\circ$
  4. $I$ lags $I_s$ by $33.69^\circ$

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Correct answer: (A) $I$ leads $I_s$ by $19.44^\circ$

Explanation

The partial current I=(0.3+j0.4)Vs has admittance angle arctan(0.4/0.3)=53.13°.

Total Is=(0.3+j0.2)Vs has angle 33.69°.

The common source phase cancels, so **I leads Is by 19.44°, A**.