Question

The particular current obtained from the solution of i in the sinusoidal response of R-C circuit is?

(a) ip = V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC))

(b) ip = -V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ-tan^-1(1/ωRC))

(c) ip = V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ-tan^-1(1/ωRC))

(d) ip = -V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC))

This question was posed to me in an internship interview.

Enquiry is from Sinusoidal Response of an R-C Circuit in portion Transients of Network Theory

Answer 1

Correct answer is (a) ip = V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC))

The best explanation: The characteristic equation consists of two parts, viz. complementary function and particular integral. The particular integral is ip = V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC)).