GATE EE 2021 Set 1 — Question 39
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Electric Circuits → Network Elements & Sources → First-Order RL & RC
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Question
In the circuit, switch 'S' is in the closed position for a very long time. If the switch is opened at time , then in amperes, for is
Correct answer
(C) 8+2e^(-10t)
Solution
For (switch S closed).The closed switch short-circuits the branch containing the resistor and the source. In steady state the inductor behaves as a short circuit, so the source drives the resistor:Inductor current cannot change instantaneously, so .For (switch S open).The circuit becomes a single loop containing the source, the source (series-aiding), the resistor, the resistor and the inductor.Total driving voltage , total resistance .Final (steady-state) current:Time constant.Transient response.This is exactly option (C). Option (A) has no steady-state term, option (B) ignores the transient, and option (D) has both the wrong final value and the wrong time constant.Answer: (C)
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