Question

The complete solution of the current in the sinusoidal response of R-C circuit is?

(a) i = e^-t/RC[V/R cosθ+V/√(R^2+(1/(ωC))^2) cos⁡(θ+tan^-1(1/ωRC))+V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC)]

(b) i = e^-t/RC[V/R cosθ-V/√(R^2+(1/ωC)^2) cos⁡(θ+tan^-1(1/ωRC))-V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC)]

(c) i = e^-t/RC[V/R cosθ+V/√(R^2+(1/ωC)^2) cos⁡(θ+tan^-1(1/ωRC))-V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC)]

(d) i = e^-t/RC[V/R cosθ-V/√(R^2+(1/(ωC))^2) cos⁡(θ+tan^-1(1/ωRC))+V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC)]

I have been asked this question in unit test.

I need to ask this question from Sinusoidal Response of an R-C Circuit topic in section Transients of Network Theory

Answer 1

Right option is (d) i = e^-t/RC[V/R cosθ-V/√(R^2+(1/(ωC))^2) cos⁡(θ+tan^-1(1/ωRC))+V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC)]

Explanation: The complete solution for the current becomes i = e^-t/RC[V/R cosθ-V/√(R^2+(1/(ωC))^2) cos⁡(θ+tan^-1(1/ωRC))+V/√(R^2+(1/ωC)^2) cos⁡(ωt+θ+tan^-1(1/ωRC)).