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

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.