Question

An inductor of 3mH has a current i = 5(1 – e^-5000t). Find the corresponding maximum energy stored. (a) 37.5 mJ (b) 375 J (c) 37.5 kJ (d) 3.75 mJ This question was addressed to me in class test. The doubt is from Basic Network Concepts in section Circuit Elements and Kirchhoff’s Laws of Network Theory

Answer 1

Correct choice is (a) 37.5 mJ Best explanation: Given L = 3 mH, i = 5(1 – e^-5000t) V = L \frac{di}{dt} = 3 × 10^{-3} \frac{d}{dt}[5(1-e^{-5000t})] = 75 e^{-5000t} I = i(∞) = 5(1 – e^-∞) = 5 A E = \frac{1}{2} LI^2 = 0.5 × 3 × 10^-3 × 5^2 = 37.5 mJ.