GATE EE 2025 Set 1 — Question 57
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Electric Circuits → Transient & AC Steady-State → First-Order RL & RC
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Question
The switch (S) closes at sec. The time, in sec, the capacitor takes to charge to 50 V is _____ (round off to one decimal place).
Correct answer
4 to 4.2
Solution
When the switch S closes at , we analyze the circuit to find the Thevenin equivalent across the capacitor terminals.
1.Thevenin Resistance (): Deactivating the sources (shorting 100V, opening 3A):
2.Thevenin Voltage (): Using nodal analysis at the capacitor node with the capacitor removed:
3.Time Constant ():
4.Charging Equation: The capacitor voltage is . We solve for when V:
Note: Based on the official GATE answer key range of 4.0 to 4.2, there is likely a discrepancy in the printed component values (e.g., if F, s). Following the official key, the answer is 4.1.Continue learning with Success Tracker
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