Question

The magnetic potential energy stored in a certain inductor is 25mJ, when the current in the inductor is 60mA. This inductor is of inductance?
1- 1.389 H
2- 0.138 H
3- 13.89 H
4- 138.88 H

Answer 1

Hint: We are given an inductor and the energy stored is 25 mJ. The current is given in mA which we have to convert it into Amperes. We can use the concept of energy stored in an inductor to solve this problem.

Complete step by step answer:
Energy stored in a Inductor is given by the formula, \[U=\dfrac{L{{i}^{2}}}{2}\]
Where L is the inductance of the inductor and I is the current passing through the inductor.
Given, L=?
U= 25 mJ = \[25\times {{10}^{-3}}J\]
i= 60 mA = \[60\times {{10}^{-3}}A\]
substituting the values in the formula we get,
$
25\times {{10}^{-3}}=\dfrac{L{{(60\times {{10}^{-3}})}^{2}}}{2} \\
\implies 50\times {{10}^{-3}}=L\times 3600\times {{10}^{-6}} \\
\therefore L=\dfrac{1000}{72}=13.88H \\
$
So, the value of inductance of the inductor is 13.89 H

So, the correct answer is “Option 3”.

Additional Information:
An inductor is an electrical component which consists of a coil. When an electric current passes through it then an induced emf is generated inside the coil. The direction of current which is produced on account of induced emf is given by Fleming's right hand rule. The magnetic field that surrounds the inductor stores energy.

Note:
An inductor is also called a choke. Inductors resist change of current but they allow steady state DC current. The SI unit of inductance is Henry. Because the Henry is a relatively large unit of inductance, for the smaller inductors sub-units of the Henry are used to denote its value.