Laplace Transform- 1 - Free MCQ Practice Test with solutions, GATE EE

Step-by-step solution

1. Write the Laplace-domain relation for an inductor
   For an inductor of inductance L with zero initial current:
   V(s) = L s I(s)

2. Express I(s) in terms of the given voltage transform
   Given V(s) = (4 s² + 3 s + 2) / (7 s² + 6 s + 5) and L = 2 H,
   I(s) = V(s) / (L s)
   = (4 s² + 3 s + 2) / [2 s (7 s² + 6 s + 5)]

3. Apply the Final-Value Theorem to find the steady current
   The final-value theorem states that i(∞) = limₜ→∞ i(t) = limₛ→0 [s I(s)], provided all poles of s I(s) lie in the left half-plane.
   So
   i(∞) = limₛ→0 [s · (4 s² + 3 s + 2) / (2 s (7 s² + 6 s + 5))]
   = limₛ→0 [(4 s² + 3 s + 2) / (2 (7 s² + 6 s + 5))]
   = 2 / 10
   = 0.2 A

4. Choose the correct option
   The steady-state current is 0.2 A (Option B).