Question

In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 100cos (103t+π/2), resistance R = 20Ω and inductance L = 0.1H. The complementary function of the solution of ‘i’ is?

(a) ic = ce^-100t

(b) ic = ce^100t

(c) ic = ce^-200t

(d) ic = ce^200t

I have been asked this question in my homework.

Question is from Sinusoidal Response of an R-L Circuit topic in chapter Transients of Network Theory

Answer 1

Right option is (c) ic = ce^-200t

For explanation: By applying Kirchhoff’s voltage law to the circuit, we have 20i+0.1di/dt=100cos⁡(10^3 t+π/2) => (D+200)i=1000cos⁡(1000t+π/2). The complementary function is ic = ce^-200t.