The property of an inductor to obtain the voltage induced by the change of current flow is defined as inductance. The ratio of the inductance voltage to the rate of change of current.

The rate of change of current produces a change in the magnetic field, which induces an emf in the direction opposite to that of the voltage source. This property involving emf is called inductance.

**The Inductance formula is:**

**Units:**

- The unit of inductance is
**henry(H)**. indicated by**L**. - Inductors are mostly available in
**mH millihenry**and**μH microhenry**.

A Henry’s inductance occurs in a coil when an emf of one volt is self-induced in the coil, where current flows at the rate of one ampere per second.

**Self-Inductance**

If a coil is considered in which some current flow, then it has some magnetic field, which is perpendicular to the current flow. When this current varies, so does the magnetic field, and this changing magnetic field, in contrast to the source voltage, induces an EMF. This opposing emf produced is self-induced voltage and this method is called self-induction.

In the figure, the current **i _{s}** indicates source current while

**i**indicates induced current. Flux represents the magnetic flux created around the coil. With the application of voltage, current flows

_{ind}**i**and flux is formed. When the current

_{s}**i**

_{s}**ch**anges, the flux obtains a varied output.

This induced EMF across the coil is proportional to the rate of change in current. The higher the rate of change of current, the higher will be the value of emf.

**We can write the above equation as:**

Where,

- E is the emf produced.
- dI/dt indicates the rate of change in current.
- L indicates the coefficient of inductance.

The coefficient of self-inductance or self-inductance can be called

The real equation is written as

The minus in the above equation indicates that the EMF is induced in the opposite direction to the voltage source according to Lenz’s law.

**Mutual Inductance**

Since a current-carrying coil produces some magnetic field around it, if another coil is brought near this coil, such that it is in the magnetic flux field of the primary, the varying magnetic flux in the second coil creates an emf. inspires. If this first horoscope is called a primary horoscope, then the second horoscope can be called a secondary horoscope.

When an emf is induced in the secondary coil due to a change in the magnetic field of the primary coil, such a phenomenon is called mutual induction.

Current **i _{s}** indicates source current while

**i**indicates induced current. The flux represents the magnetic flux built up around the coil. It also spreads to the secondary coil.

_{ind}With the application of voltage, the current **i _{s}** flows and builds up. When the current

**i**changes, the flux in the secondary coil produces

_{s}**i**different outputs, due to the mutual inductance property.

_{ind}**This is how the change happened:**

**Vp Ip → B → Vs Is**

Where,

**Vp ip**indicates voltage and current respectively in the primary coil.**B**indicates magnetic flux.indicates the voltage and current in the secondary coil respectively.**Vs Is**

The mutual inductance M of the two circuits describes the amount of voltage across the secondary induced by a change in the primary’s current.

where ΔI/Δt is the rate of change of current with time and M is the coefficient of mutual inductance. The minus sign indicates that the direction of the current is opposite to that of the source.

**Units −**

The units of mutual inductance are:

Depending on the number of turns of the primary and secondary coils, the amount of magnetic flux linkage and induced emf varies. The number of turns in the primary is denoted by N1 and in the secondary by N2. Coefficient of coupling is the term that specifies the mutual inductance of two coils.

**Factors Affecting Inductance**

There are a few factors that affect the performance of an inductor. The major ones are discussed below.

**Length of the coil**

The length of the inductor coil is inversely proportional to the inductance of the coil. If the length of the coil is greater, the inductance delivered by that inductor is reduced and vice versa.

**Cross-sectional area of the coil**

The area of the cross-section of the coil is proportional to the inductance of the coil. The greater the area of the coil, the greater the inductance.

**Number of turns**

Along with the number of turns, the coil directly affects the inductance. The value of inductance becomes the square of the number of turns of the coil. Therefore, the greater the number of turns, the value of the inductance of the square coil will be.

**Permeability of the core**

The permittivity μ of the core material of the inductor indicates the support that the core provides for the formation of a magnetic field within itself. The higher the permeability of the core material, the higher the inductance.

**Coefficient of Coupling**

This is an important factor known to calculate the mutual inductance of two coils. Let us consider two adjacent coils of turns N1 and N2 respectively.

The current through the first coil i_{1} produces some flux Ψ_{1}. The amount of magnetic flux linkage is understood by Weber-Turn.

The amount of magnetic flux attached to the second coil due to unit current of i_{1} is

It can be understood as the coefficient of mutual inductance, which means

Hence the coefficient of mutual inductance between two coils or circuits is understood as the Weber-turn in one coil due to 1A current in the other coil.

If the self inductance of the first coil is L1, then

Similarly, the coefficient of mutual inductance due to current i_{2} in the second coil is

If the self-inductance of the second coil is L2

Therefore,

On multiplying 1 and 2, we get

The above equation is true when the entire variable current of the primary coil connects to the secondary coil, which is an ideal situation. But in practice it is not so. Therefore, we can write as

where K is known as the coefficient of coupling.

The coefficient of coupling can be defined as the ratio of the actual coefficient of mutual inductance to the ideal maximum coefficient of mutual inductance.

If the value of k is close to unity, then the coils are said to be tightly coupled, and if the value of k = 0, then the coils are said to be loosely coupled.

**Applications of Inductors**

Inductors have many applications, such as –

- Inductors are used in filter circuits to sense high frequency components and suppress noisy signals.
- To isolate the circuit from unwanted HF signals.
- Inductors are used in electrical circuits to form transformers and to isolate the circuit from spikes.
- Inductors are also used in motors.