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 complementary function of the solution of ‘i’ is?

(a) ic = c exp (-t/10^-10)

(b) ic = c exp(-t/10^10)

(c) ic = c exp (-t/10^-5)

(d) ic = c exp (-t/10^5)

The question was posed to me in final exam.

Origin of the question is Sinusoidal Response of an R-C Circuit in portion Transients of Network Theory

Answer 1

The correct choice is (c) ic = c exp (-t/10^-5)

To elaborate: By applying Kirchhoff’s voltage law to the circuit, we have

(D+1/10^-5) )i=-500sin⁡(1000t+π/4). The complementary function is ic = c exp (-t/10^-5).