Question

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

(a) i = e^-t(R/L)[V/√(R^2+(ωL)^2) cos⁡(θ-tan^-1)⁡(ωL/R))]+V/√(R^2+(ωL)^2) cos⁡(ωt+θ-tan^-1)⁡(ωL/R))

(b) i = e^-t(R/L)[-V/√(R^2+(ωL)^2) cos⁡(θ-tan^-1)(ωL/R))]-V/√(R^2+(ωL)^2) cos⁡(ωt+θ-tan^-1)⁡(ωL/R))

(c) i = e^-t(R/L)[V/√(R^2+(ωL)^2) cos⁡(θ-tan^-1)⁡(ωL/R))]-V/√(R^2+(ωL)^2) cos⁡(ωt+θ-tan^-1)⁡(ωL/R))

(d) i = e^-t(R/L)[-V/√(R^2+(ωL)^2) cos⁡(θ-tan^-1)⁡(ωL/R))]+V/√(R^2+(ωL)^2) cos⁡(ωt+θ-tan^-1)⁡(ωL/R))

The question was asked in final exam.

This intriguing question originated from Sinusoidal Response of an R-L Circuit topic in portion Transients of Network Theory

Answer 1

Correct answer is (d) i = e^-t(R/L)[-V/√(R^2+(ωL)^2) cos⁡(θ-tan^-1)⁡(ωL/R))]+V/√(R^2+(ωL)^2) cos⁡(ωt+θ-tan^-1)⁡(ωL/R))

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