Question

In the circuit shown, VC is zero at t=0 s. For t>0, the capacitor current IC(t), where t is in second, is ___________ (a) 0.50 e^-25t mA (b) 0.25 e^-25t mA (c) 0.50 e^-12.5t mA (d) 0.25 e^-6.25t mA I had been asked this question in an interview. My enquiry is from Advanced Problems on Network Theorems in section Useful Theorems in Circuit Analysis of Network Theory Select the correct answer from above options network theory questions and answers, network theory questions pdf, network theory question bank, network theory gate questions and answers pdf, mcq on network theory pdf, gate network theory questions and solutions, network theory mcq Test , ies network theory questions, Network theory Questions for GATE EC Exam, Network Theory MCQ (Multiple Choice Questions)

Answer 1

Correct choice is (a) 0.50 e^-25t mA Easiest explanation: The capacitor voltage VC (t) = VC (∞) – [VC (∞)-VC (0)]e^-t/RC R = 20 || 20 = \frac{20×20}{20+20} = \frac{400}{40} = 10 kΩ VC (∞) = 10 × \frac{20}{20+20} = 5 V Given, VC (0) = 0 ∴ VC (t) = 5 – (5-0)e^-t/10×4×10^(-6)×10^3 = 5(1 – e^-25t) IC (t) = C\frac{dV_C (t)}{dt} = 4×10^{-6} \frac{d}{dt}5(1-e^{-25t}) = 4 × 10^-6 × 5 × 25e^-25t ∴ IL (t) = 0.50e^-2.5t mA.