GATE 2016 EE (EE2) – Question 47

The capacitor initially has 4 V. S1 closes at t=0. The charge lost between t=25 μs and t=100 μs, in μC, is ________.

Show answer and explanation

Correct answer: 6.8 to 7.2

Explanation

The discharge time constant is RC=5 Ω×5 μF=25 μs. Initial charge is CV0=20 μC, so Q(t)=20e⁻ᵗ/²⁵ μC when t is in μs.

Charge lost over the specified interval is $20(e^{-1}-e^{-4})=$ **6.99128 μC**, within 6.8–7.2. The charge already lost before 25 μs is excluded.

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