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GATE 2024 EE – Question 14

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 · 1 mark · Multiple choice

The circuit shown in the figure with the switch $S$ open, is in steady state. After the switch $S$ is closed, the time constant of the circuit in seconds is

Diagram for GATE 2024 EE question 14
  1. 1.25
  2. 0
  3. 1
  4. 1.5

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Show answer and explanation

Correct answer: (A) 1.25

Explanation

For the time constant the ideal 1 A source is replaced by an open circuit. With S closed, the remaining circuit is a single loop containing the left (1 Ω, 1 H) branch, the (1 Ω, 1 H) branch through the switch, and the two 1 H inductors in parallel ($0.5$ H). Total $R=1+1=2\ \Omega$ and total $L=1+1+0.5=2.5$ H, so $\tau=L/R=1.25$ s.