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
Before the switch closes ().
With S open no current can flow through the 5 F capacitor branch, so there is no drop across the 2 resistor and the left plate of the capacitor sits at V above the bottom rail. The 3 A source circulates entirely through the 25 resistor, so the right-hand node (right plate of the capacitor) is atabove the bottom rail. Hence the initial capacitor voltage isAfter the switch closes ().
S short-circuits that node to the bottom rail, which places a short across both the 25 resistor and the 3 A source. Neither of them can then influence the capacitor branch. What is left is a simple loop:SoTransient.Set V:Answer: approximately s
With S open no current can flow through the 5 F capacitor branch, so there is no drop across the 2 resistor and the left plate of the capacitor sits at V above the bottom rail. The 3 A source circulates entirely through the 25 resistor, so the right-hand node (right plate of the capacitor) is atabove the bottom rail. Hence the initial capacitor voltage isAfter the switch closes ().
S short-circuits that node to the bottom rail, which places a short across both the 25 resistor and the 3 A source. Neither of them can then influence the capacitor branch. What is left is a simple loop:SoTransient.Set V:Answer: approximately s
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