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

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).