GATE EC 2023 Set 1 — Question 44
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Network Theory → Transient & AC Analysis → RL, RC & RLC Transients
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Question
The switch was closed and was open for a long time. At , switch is opened and is closed, simultaneously. The value of , in amperes, is
Correct answer
(B) -1
Solution
1.Analyze the circuit for (Steady State):
- Switch is closed and is open.
- Since is open, the branch containing the resistor and inductor is an open circuit. Thus, .
- In DC steady state, the capacitor acts as an open circuit. The current from the source flows entirely through the resistor.
- The voltage across the capacitor is the same as the voltage across the resistor: .
- Switch is opened (disconnecting the source) and is closed.
- By continuity of state variables: and .
- Apply Kirchhoff's Current Law (KCL) at the top node at :
- Since , .
- The current through the resistor is .
- Substituting these into the KCL equation:
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