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GATE 2025 EC – Question 39

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

In the circuit below, $M_1$ is an ideal AC voltmeter and $M_2$ is an ideal AC ammeter. The source voltage (in Volts) is $v_s(t)=100\cos(200t)$.

What should be the value of the variable capacitor $C$ such that the RMS readings on $M_1$ and $M_2$ are 25 V and 5 A, respectively?

Diagram for GATE 2025 EC question 39
  1. 25 μF
  2. 4 μF
  3. 0.25 μF
  4. Insufficient information to find $C$

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Show answer and explanation

Correct answer: (A) 25 μF

Explanation

The voltmeter reads the voltage across the 5 Ω–$C$–1 H series branch and the ammeter reads its current, so the magnitude of the branch impedance is $25/5=5\ \Omega$. Since the resistance alone is 5 Ω, the reactance must be zero: $\omega L=1/(\omega C)$. With $\omega=200$ rad/s and $L=1$ H, $C=1/(\omega^2L)=1/(40000)=25\ \mu$F.