Question

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

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

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

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

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

The question was posed to me in examination.

This key question is from Sinusoidal Response of an R-L Circuit topic in chapter Transients of Network Theory

Answer 1

Right answer is (b) ip = V/√(R^2+(ωL)^2) cos⁡(ωt+θ-tan^-1(ωL/R))

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