Question

A pulse of unit amplitude and width a, is applied to a series RL circuit having R = 1 Ω, L = 1H. The current I(t) at t = ∞ is __________

(a) 0

(b) Infinite

(c) 2 A

(d) 1 A

The question was asked in unit test.

I need to ask this question from Fourier Analysis in division Fourier Analysis on Complex Spaces of Signals and Systems

Answer 1

Right choice is (a) 0

Easy explanation: Since, the circuit has a resistance; the current will eventually decrease and ultimately die down.

Now, I (t) = \((\frac{1}{R})[u (t) (1-e^{\frac{-Rt}{L}}) – u (t-a) (1-e^{\frac{-R(t-a)}{L}})]\)

But R = 1Ω and L = 1H

∴ I(t) = [u(t)(1-e^-t) – u(t-a)(1-e^-(t-a))]

This also leads to I (∞) = 0.