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GATE 2022 EC – Question 39

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

Consider the circuit shown in the figure with input $V(t)$ in volts. The sinusoidal steady state current $I(t)$ flowing through the circuit is shown graphically (where $t$ is in seconds). The circuit element $Z$ can be ________.

Diagram for GATE 2022 EC question 39
  1. a capacitor of 1 F
  2. an inductor of 1 H
  3. a capacitor of $\sqrt3$ F
  4. an inductor of $\sqrt3$ H

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Show answer and explanation

Correct answer: (B) an inductor of 1 H

Explanation

The current amplitude is $\frac{1}{\sqrt2}$ A for a 1 V source at $\omega=1$ rad/s, so $|1+Z|=\sqrt2$, which with the $1\ \Omega$ resistor means $|X|=1\ \Omega$. The plot shows $I(t)$ crossing zero while rising at $t=\pi/4$, so $I=\frac1{\sqrt2}\sin(t-\pi/4)$ lags the voltage by $45^\circ$, which needs an inductive element. $\omega L=1$ gives $L=1$ H.