GATE EC 2017 Set 2 — Question 31
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Network Theory → Transient & AC Analysis → RL, RC & RLC Transients
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Question
The switch in the circuit, shown in the figure, was open for a long time and is closed at .
The current (in ampere) at seconds is ___________
Correct answer
8 to 8.3
Solution
1.Initial State (): The switch is open. The circuit is in steady state, so the inductor acts as a short circuit. The 10 A current splits between the two parallel branches (each having a 5 resistance). The current through the inductor branch is .
2.Transient State (): The switch is closed at . This shorts the nodes, making the voltage across all parallel branches zero. The 5 resistor in the middle branch is shorted, so its current is zero. The 10 A source current now flows through the short (switch branch).
3.Inductor Current Decay: The inductor branch (5 resistor and 2.5 H inductor) is now a closed loop with zero external voltage. The current decays as .
4.Switch Current : Applying KCL at the top node: .
5.Calculation at : .
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