1.

The particular current obtained from the solution of i in the sinusoidal response of R-L-C circuit is?(a) ip = V/√(R^2+(1/ωC+ωL)^2) cos⁡(ωt+θ+tan^-1)⁡((1/ωC+ωL)/R))(b) ip = V/√(R^2+(1/ωC-ωL)^2) cos⁡(ωt+θ+tan^-1)⁡((1/ωC-ωL)/R))(c) ip = V/√(R^2+(1/ωC+ωL)^2) cos⁡(ωt+θ+tan^-1)⁡((1/ωC-ωL)/R))(d) ip = V/√(R^2+(1/ωC-ωL)^2) cos⁡(ωt+θ+tan^-1)⁡((1/ωC+ωL)/R))The question was posed to me in unit test.My doubt stems from Sinusoidal Response of an R-L-C Circuit in portion Transients of Network Theory

Answer»

Correct OPTION is (B) ip = V/√(R^2+(1/ωC-ωL)^2) cos⁡(ωt+θ+tan^-1)⁡((1/ωC-ωL)/R))

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



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