GATE EC 2021 Set 1 — Question 48
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Network Theory → Transient & AC Analysis → RL, RC & RLC Transients
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Question
In the circuit shown in the figure, the switch is closed at time , while the capacitor is initially charged to (i.e., ).
The source is , the series resistor (across which is measured) is , the shunt resistor is , the dependent current source carries (in A), and the capacitance is .The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is ________ ms.
Correct answer
0.132 to 0.146
Solution
For , find the Thévenin equivalent seen by the capacitor. Let be the voltage at the top of the shunt resistor, so .Open-circuit voltage: KCL at the node:Short-circuit current: with , V. Current in from the series resistor is mA, the dependent source takes mA and the shunt resistor takes 0, so mA.Capacitor voltage:Setting : , so ms.Answer: 0.139 ms
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