Question

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

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

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

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

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

I got this question by my college director while I was bunking the class.

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

Answer 1

The correct choice is (d) c = V/R cosθ-V/√(R^2+(1/(ωC))^2) cos⁡(θ+tan^-1(1/ωRC))

The best I can explain: Since the capacitor does not allow sudden changes in voltages, at t = 0, i = V/R cosθ. So, c = V/R cosθ-V/√(R^2+(1/(ωC))^2) cos⁡(θ+tan^-1(1/ωRC)).