Question

In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 100cos (103t+π/2), resistance R = 20Ω and inductance L = 0.1H. The particular integral of the solution of ‘ip’ is? (a) ip = 0.98cos⁡(1000t+π/2-78.6^o) (b) ip = 0.98cos⁡(1000t-π/2-78.6^o) (c) ip = 0.98cos⁡(1000t-π/2+78.6^o) (d) ip = 0.98cos⁡(1000t+π/2+78.6^o) This question was addressed to me during a job interview. My question comes from Sinusoidal Response of an R-L Circuit topic in division Transients of Network Theory Select the correct answer from above options network theory questions and answers, network theory questions pdf, network theory question bank, network theory gate questions and answers pdf, mcq on network theory pdf, gate network theory questions and solutions, network theory mcq Test , ies network theory questions, Network theory Questions for GATE EC Exam, Network Theory MCQ (Multiple Choice Questions)

Answer 1

The correct option is (a) ip = 0.98cos⁡(1000t+π/2-78.6^o) For explanation: Assuming particular integral as ip = A cos (ωt + θ) + B sin(ωt + θ). We get ip = V/√(R^2+(ωL)^2) cos⁡(ωt+θ-tan^-1(ωL/R)) where ω = 1000 rad/sec, V = 100V, θ = π/2, L = 0.1H, R = 20Ω. On substituting, we get ip = 0.98cos⁡(1000t+π/2-78.6^o).