Question

For a unit step signal u (t), the response is V1 (t) = (1-e^-3t) for t>0. If a signal 3u (t) + δ(t) is applied, the response will be (considering zero initial conditions)? (a) (3-6e^-3t)u(t) (b) (3-3e^-3t)u(t) (c) 3u(t) (d) (3+3e^-3t)u(t) The question was asked in a job interview. My query is from Dot Convention in Magnetically Coupled Circuits in chapter Resonance & Magnetically Coupled Circuit 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

Correct option is (c) 3u(t) Explanation: For u (t) = 1, t>0 V1 (t) = (1-e^-3t) Or, V1 (s) = \left(\frac{1}{s} + \frac{1}{s+3}\right) = \frac{3}{s(s+3)} And T(s) = \frac{V_1 (S)}{u(S)} = \frac{3}{s+3} Now, for R(s) = (\frac{3}{s} + 1) Response, H(s) = R(s) T(s) = (\frac{3+s}{s}) (\frac{3}{s+3}) = \frac{3}{s} Or, h (t) = 3 u (t).