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

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

1.	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» 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)).

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