Induction - Definition, Difference, FAQs

What is Inductance?

Inductance refers to an electrical conductor’s capability to withstand the changes in electric current passing through it. L is the symbol to represent inductance and its SI unit is Henry. One Henry is defined as the quantity of inductance whereby an induced emf of 1 volt appears in a coil of wire carrying out a change in current of 1 ampere/second.

Factors Affecting Inductance

• Inductance is affected by the following factors:
• The inductor turns to measure how many turns there are in the wire.
• In the core is a material used.
• The shape of the core.

Types of Inductance

Inductance is classified into two types:

• Self Induction
• Mutual Induction

Self Induction

The electromotive force is created whenever there is a variation in either the electrical current or the magnetic flux of the coil. Such a process is known as Self-Inductance. At any instant when the current begins to increase in the coil, the magnetic flux is found to vary directly with the current in the circuit. The relationship is expressed as:

$$
\phi=L \times I
$$
Where $L$ is termed as the self-inductance of the coil or the coefficient of self-inductance, the self-inductance depends on the cross-sectional area, the permeability of the material, and the number of turns in the coil.

The rate of change of magnetic flux in the coil is given as,

$$
\begin{aligned}
& e=-\frac{d \phi}{d t}=-\frac{d(L I)}{d t} \\
& e=-L \frac{d I}{d t}
\end{aligned}
$$

Self Inductance Formula

$$
L=N \frac{\phi}{T}
$$
Where,
Lis the self-inductance in Henries
N is the number of turns
$\Phi$ is the magnetic flux
I is the current in amperes

Mutual Induction

Let us consider two coils. The first coil will be referred to as the P- coil (Primary coil) and the second will be is S- coil (Secondary coil). A battery and a key are connected to the P-coil, while a galvanometer is connected across the S-coil. Whenever there is a change in the provided current or the magnetic flux associated with both coils, then in each coil an electromotive force appears which opposes the change, this is called Mutual Inductance.

This phenomenon is given by the relation:

$$
\phi=M I
$$
Where $M$ is termed as the mutual inductance of the two coils or the coefficient of the mutual inductance of the two coils.

The rate of change of magnetic flux in the coil is given as,

$$
\begin{aligned}
& e=-\frac{d \phi}{d t}=-\frac{d(M I)}{d t} \\
& e=-M \frac{d I}{d t}
\end{aligned}
$$

Mutual Inductance Formula

$$
M=\frac{\mu_0 \mu_1 N_1 N_2 A}{l}
$$
Where,
$\mu_0$ is the permeability of free space
$\mu_r$ is the relative permeability of the soft iron core
N is the number of turns in the coil
$A$ is the cross-sectional area in $\mathrm{m}^2$
I is the length of the coil in $m$

Difference Between Self-Inductance and Mutual Inductance

Also read :

• NCERT Solutions for All Subjects
• NCERT Notes For All Subjects
• NCERT Exemplar Solutions for All Subjects

Derivation of Inductance

Consider a DC source. When the switch is turned on, the current flows from zero to a certain value such that there is a change in the rate of current flowing. Let $\phi$ be the change in flux due to current flow. The change in flux is with respect to time which is given as:

$$
\frac{d \varphi}{d t}
$$
Apply Faraday's law of electromagnetic induction,

$$
E=N \frac{d \phi}{d t}
$$
Where,
N is the number of turns in the coil
E is the induced EMF across the coil

From Lenz's law, we can write the above equation as

$$
E=-N \frac{d \phi}{d t}
$$
The above equation is modified for calculating the value of inductance

$$
\begin{aligned}
& E=-N \frac{d \phi}{d t} \\
& E=-L \frac{d i}{d t}
\end{aligned}
$$