Question

In the sinusoidal response of R-L-C circuit, the complementary function of the solution of i is?

(a) ic = c1 e^(K1+K2)t + c1 e^(K1-K2)t

(b) ic = c1 e^(K1-K2)t + c1 e^(K1-K2)t

(c) ic = c1 e^(K1+K2)t + c1 e^(K2-K1)t

(d) ic = c1 e^(K1+K2)t + c1 e^(K1+K2)t

I have been asked this question in an interview for internship.

My question is taken from Sinusoidal Response of an R-L-C Circuit in chapter Transients of Network Theory

Answer 1

Right answer is (a) ic = c1 e^(K1+K2)t + c1 e^(K1-K2)t

Easiest explanation: From the R-L circuit, we get the characteristic equation as

(D^2+R/L D+1/LC)=0. The complementary function of the solution i is                                                           ic = c1 e^(K1+K2)t + c1 e^(K1-K2)t.