Q. In an $L - R$ circuit to a battery, the rate at which energy is stored in the inductor is plotted against time during the growth of current in the circuit. Which of the following, figure best represents the resulting curve?
A) [image:7_image17.png]
B) [image:7_image18.png]
C) [image:7_image19.png]
D) [image:7_image20.png]
Explanation
(c) Energy stored in a inductor $L\ $carrying
Current $i\ is\ U = \frac{1}{2}\ L\ i^{2}$
Rate at which energy is stored
$= \frac{dU}{dt} = \frac{1}{2}\ L\ 2i\ \left( \frac{di}{dt} \right) = Li\ \left( \frac{di}{dt} \right)\ $
At $t = 0,\ i = 0,\ \ \ \ \ \ \ \therefore\ \frac{dU}{dt} = 0\ $
At $t\ = \ \infty,\ i = i_{0}\ (constant),\ \ \ \therefore\ \ \frac{di}{dt} = 0\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.