The GATE Grind

GATE 2025 EE – Question 57

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 2 marks · Numerical answer

The switch (S) closes at $t=0$ sec. The time, in sec, the capacitor takes to charge to 50 V is _____ (round off to one decimal place).

Diagram for GATE 2025 EE question 57

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 6.87 to 6.93

Explanation

Closing S short-circuits the 25 Ω resistor and the 3 A source, leaving the 100 V source charging the 5 F capacitor through the 2 Ω resistor from zero initial voltage: $v_c=100(1-e^{-t/ au})$ with $ au=RC=2 imes5=10$ s. It reaches 50 V when $e^{-t/ au}=0.5$, i.e. $t=10ln2=6.9$ s.