Question

A coil of inductance 10 H, resistance 40 Ω is connected as shown in the figure. After the switch S has been in connection with point 1 for a very long time, it is moved to point 2 at t=0. For the value of R obtained, the time taken for 95 % of the stored energy dissipated is close to?

(a) 0.10 s

(b) 0.15 s

(c) 0.50 s

(d) 1.0 s

I have been asked this question in exam.

My question comes from Fourier Series Analysis using Circuits in division Fourier Analysis on Complex Spaces of Signals and Systems

Answer 1

The correct choice is (c) 0.50 s

Explanation: For source free circuit,

I (t) = Io \(e^{-\frac{R}{T} \,t}\)

∴ I (t) = 0.05 = 2 × \(e^{-\frac{60}{10} \,t}\)

Or, t = 0.61 ≈ 0.5 s.