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GATE 2026 EC – Question 39

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

In the given circuit, $L=1$ μH and $C=1$ μF. The phasor diagram for $I_C$ and $I_L$ is also shown. Assume that the phase ($\theta_1+\theta_2$) is 90° at a frequency of 159.15 kHz. Among the following options, what is the nearest integer value of $R_C\times R_L$?

Diagram for GATE 2026 EC question 39
  1. 0
  2. 1
  3. 2
  4. 10

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Correct answer: (B) 1

Explanation

At 159.15 kHz, $\omega=10^6$ rad/s, so $X_L=\omega L=1\ \Omega$ and $X_C=1/(\omega C)=1\ \Omega$. Then $\tan\theta_1=1/R_C$ and $\tan\theta_2=1/R_L$. With $\theta_1+\theta_2=90^\circ$, $\tan\theta_1\tan\theta_2=1$, so $R_CR_L=1$.