Energy in an inductor: At a certain instant the current flowing through a 5.0-H inductor is 3.0 A. If the energy in the inductor at this instant is increasing at a rate of 3.0 J/s, how fast is the current changing?
A) 0.20 A/s
B) 0.40 A/s
C) 0.10 A/s
D) 0.80 A/s

Question

Quizplus · Accepted Answer

The energy stored in an inductor is given by $ E = \frac{1}{2} L I^2 $. Differentiating with respect to time, $ \frac{dE}{dt} = L I \frac{dI}{dt} $. Given $ \frac{dE}{dt} = 3.0 \, \text{J/s} $, $ L = 5.0 \, \text{H} $, and $ I = 3.0 \, \text{A} $, we solve for $ \frac{dI}{dt} $: $ 3.0 = 5.0 \times 3.0 \times \frac{dI}{dt} $, leading to $ \frac{dI}{dt} = 0.20 \, \text{A/s} $.

Energy in an Inductor: at a Certain Instant the Current