Question

In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The complete solution of ‘i’ is?

(a) i = c exp (-t/10^-5) – (4.99×10^-3) cos⁡(100t+π/2+89.94^o)

(b) i = c exp (-t/10^-5) + (4.99×10^-3) cos⁡(100t+π/2+89.94^o)

(c) i = -c exp(-t/10^-5) + (4.99×10^-3) cos⁡(100t+π/2+89.94^o)

(d) i = -c exp(-t/10^-5) – (4.99×10^-3) cos⁡(100t+π/2+89.94^o)

The question was asked in an online interview.

I'm obligated to ask this question of Sinusoidal Response of an R-C Circuit topic in division Transients of Network Theory

Answer 1

The correct option is (b) i = c exp (-t/10^-5) + (4.99×10^-3) cos⁡(100t+π/2+89.94^o)

Easy explanation: The complete solution for the current is the sum of the complementary function and the particular integral. The complete solution for the current becomes  i = c exp (-t/10^-5) + (4.99×10^-3)  cos⁡(100t+π/2+89.94^o).