JEE Main Syllabus 2025 PDF - Subject Wise Topics

# Energy Stored In An Inductor - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Energy stored in an inductor is considered one the most difficult concept.

• 8 Questions around this concept.

## Solve by difficulty

$0.1 \mathrm{~m}$ long conductor carrying a current  $50 \mathrm{~A}$ is held perpendicular to a magnetic field $1.25 \mathrm{mT}$. The mechanical power required to move the conductor with a speed of $1 \mathrm{~ms}^{-1}$ is:

A current of 1 A through a coil of inductance of 200 mH is increasing at a rate of $\mathrm{0.5 \mathrm{~A} \mathrm{~s}^{-1}}$ . The energy stored in the inductor per second is:

Shown in the figure is a parallel R, L, C circuit with key K1 closed and K2 opened. When K1 is opened and K2 is closed simultaneously , The maximum charge stored in it is:

## Concepts Covered - 1

Energy stored in an inductor

Energy stored in an inductor (U)-

In building a steady current in the circuit, the source emf has to do work against of self-inductance of the coil and whatever energy
consumed for this work stored in the magnetic field of coil this energy called as magnetic potential energy (U) of the coil.

When an electric current i is flowing in an inductor, there is energy stored in the magnetic field. Considering a pure inductor L, the instantaneous power which must be supplied to initiate the current in the inductor is

$P=i v=L i \frac{d i}{d t}$

The work done by the voltage source during a time interval  is

$d W=P d t= i L \frac{d i}{d t} d t=L i d i$

total work  done in establishing the final current  in the inductor

$\text { W }=\int_{0}^{t} P d t=\int_{0}^{I} L i d i =\frac{1}{2} L I^{2}$

So Energy stored in the magnetic field of the inductor is given as

$U= \frac{1}{2}LI^{2}$

The energy density (u)/Energy per unit volume-

using $U= \frac{1}{2}LI^{2}$

for the solenoid field, we can write

$U=\frac{1}{2}(L i) i=\frac{N \phi i}{2}$

$u=\frac{U}{V}= \frac{B^{2}}{2\mu _{0}}$

## Study it with Videos

Energy stored in an inductor

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