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 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
To find the time when the capacitor voltage becomes zero, we first determine the Thévenin equivalent circuit seen by the capacitor for .
Since , we have:
. The test current is:
Setting , , and :
Rounding to three decimal places, the time is .
1.Thévenin Voltage ():
With the switch open, let the node voltage at the switch be . Applying KCL at node :Since , we have:
2.Thévenin Resistance ():
Shorting the 5V source and applying a test voltage at the switch node:. The test current is:
3.Time Constant ():
4.Capacitor Voltage Equation:
Setting , , and :
Rounding to three decimal places, the time is .
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