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GATE 2021 EE – Question 39

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 2 marks · Multiple choice

In the circuit, switch 'S' is in the closed position for a very long time. If the switch is opened at time $t=0$, then $i_L(t)$ in amperes, for $t\ge0$ is

Diagram for GATE 2021 EE question 39
  1. $8e^{-10t}$
  2. 10
  3. $8+2e^{-10t}$
  4. $10(1-e^{-2t})$

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Correct answer: (C) $8+2e^{-10t}$

Explanation

With S closed the $4\ \Omega$-30 V branch is shorted, so $i_L(0^-)=\frac{10}{1}=10$ A. After opening, the two sources add in series: $\frac{10+30}{4+1}=8$ A final current. The time constant is $\frac{L}{R}=\frac{0.5}{5}=0.1$ s, so $i_L=8+(10-8)e^{-10t}=8+2e^{-10t}$.