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 value of c in the complementary function of ‘i’ is?

(a) c = (3.53-4.99×10^-3) cos⁡(π/4+89.94^o)

(b) c = (3.53+4.99×10^-3) cos⁡(π/4+89.94^o)

(c) c = (3.53+4.99×10^-3) cos⁡(π/4-89.94^o)

(d) c = (3.53-4.99×10^-3) cos⁡(π/4-89.94^o)

I had been asked this question in a national level competition.

My question comes from Sinusoidal Response of an R-C Circuit in section Transients of Network Theory

Answer 1

Correct option is (a) c = (3.53-4.99×10^-3) cos⁡(π/4+89.94^o)

Easiest explanation: At t = 0, the current flowing through the circuit is 3.53A. So, c = (3.53-4.99×10^-3)  cos⁡(π/4+89.94^o).