# What is Inductor and Inductance | Theory of Inductor

Posted by Sibasish Ghosh on 24/2/2012 & Updated on 19/8/2018## What is Inductor?

Before knowing**what is inductor**we should first know the

**definition of inductance**.

#### Definition of Inductance

If a changing flux is linked with a coil of a conductor there would be an emf induced in it. The property of the coil of inducing emf due to the changing flux linked with it is known as**inductance of the coil**. Due to this property all electrical coil can be referred as

**inductor**. In other way, an inductor can be defined as an energy storage device which stores energy in form of magnetic field.

## Theory of Inductor

A current through a conductor produces a magnetic field surround it. The strength of this field depends upon the value of current passing through the conductor. The direction of the magnetic field is found using the right hand grip rule, which shown. The flux pattern for this magnetic field would be number of concentric circle perpendicular to the detection of current.Now if we wound the conductor in the form of a coil or solenoid, it can be assumed that there will be concentric circular flux lines for each turn of the coil as shown. But it is not possible practically, as if concentric circular flux lines for each turn exist, they will intersect each other. However, since lines of flux cannot intersect, the flux lines for an individual turn will distort to form complete flux loops around the whole coil as shown. This flux pattern of a current carrying coil is similar to a flux pattern of a bar magnet as shown.

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Now if the current through the coil is changed, the magnetic flux produced by it will also be changed at the same rate. As the flux already surrounds the coil, this changing flux obviously links the coil. Now according to Faraday’s law of electromagnetic induction, if changing flux links with a coil, there would be an induced emf in it. Again as per Lenz’s law, this induced emf opposes every cause of producing it. Hence, the induced emf is in opposite of the applied voltage across the coil.

### Definition of Self Inductance

Whenever current flows through a circuit or coil, flux is produced surround it, and this flux also links with the coil itself. Self-induced emf in a coil is produced due to its own changing flux and changing flux is caused by changing current in the coil. So, it can be concluded that self-induced emf is ultimately due to changing current in coil itself. And self-inductance is the property of a coil or solenoid, which causes a self-induced emf to be produced when the current through it changes.### Explanation of Self Inductance of a Coil

Whenever changing flux, links with a circuit, an emf is induced in the circuit. This is Faraday’s laws of electromagnetic induction. According to this law, Where e is the induced emf. N is the number of turns. (dφ/dt) is the rate of change of flux leakage with respect to time. The negative sign of the equation indicates that the induced emf opposes the change flux linkage. This is according to Lenz's law of induction. The flux is changing due to the change in current of the circuit itself. The produced flux due to a current, in a circuit, always proportional to that current. That means, Where i is the current in the circuit and K is the proportional constant. Now, from equation (1) and (2) we get, The above equation can also be rewritten as Where L (= NK) is the constant of proportionality, and this L is defined as the self-inductance of the coil or solenoid. This L determines how much emf will be induced in a coil for a specific rate of change of current through it.Now, from equation (1) and (3), we get,
Integrating, both sides we get,
From the above expression, the inductance can also be defined as,
“If the current I through an N turn coil produces a flux of Ø Weber, then its self-inductance would be L.”
A coil can be designed to have a specific value of self-inductance (L). In the view of self-inductance, a coil or solenoid is referred to as an inductor. Now, if the cross-sectional area of the core of the inductor(coil) is A and flux density in the core is B, then total flux inside the core of inductor is AB.
Therefore, equation (4) can be written as
Now, B = μ_{o}μ_{r}H Where, H is magnetic field strength, µ_{o} and μ_{r} are permeability of free space and relative permeability of the core respectively. Now, H = mmf/unit length = Ni/l Where l is the length of the coil. Therefore,

### Self Inductance Formula

### Video presentation on theory of Inductor

### Unit of Inductance

Which we derived at equation (3). Where, L is known is the self induction of the circuit. In the above**equation of inductance**, if e = 1 Volt and (di / dt) is one ampere per second, then L = 1 and its unit is Henry. That means, if a circuit, produces emf of 1 Volt, due to the rate of change of current through it, one ampere per second then the circuit is said to have one henry self-inductance. This henry is

**unit of inductance**.

## Mutual Inductance

**Inductance**due to the current, through the circuit itself is called self-inductance. But when a current flows through a circuit nearer to another circuit, then flux due to first circuit links to the secondary circuit. If this flux linkage changes with respect to time, there will be an induced emf in the second circuit. Similarly, if current flows through the second circuit, it will produce flux, and if this current changes, the flux will also change. This changing flux will link with the first coil. Due to this phenomenon, emf will be induced in the first coil. This phenomenon is known as mutual inductance. If current i

_{1}flows through circuit 1 then emf e

_{2}is induced in the nearby circuit is given by, Where M is the mutual inductance. If current i

_{2}flows through circuit 2, then emf e

_{1}is induced in the nearby circuit 1 is given by,

### Defination of Mutual Inductance

Mutual inductance may be defined as the ability of one circuit to produce an emf in a nearby circuit by induction when the current in the first circuit changes. Reversely, the second circuit can also induce emf in the first circuit if the current in the second circuit changes.### Coefficient of Mutual Inductance

Let’s consider two nearby coils of turns N_{1}and N

_{2}respectively. Let us again consider, current i

_{1}flowing through first coil produces φ

_{1}. If this whole of the flux links with the second coil, the weber-turn in the second coil would be N

_{2}φ

_{1}due to current i

_{1}in the first coil. From this, it can be said, (N

_{2}φ

_{1})/i

_{1}is the weber-turn of the second coil due to unit current in the first coil. This term is defined as the coefficient of mutual inductance. That means mutual inductance between two coils or circuits is defined as the weber-turns in one coil or circuit due to 1 A current in the other coil or circuit.

### Formula or Equation of Mutual Inductance

Now we have already found that mutual inductance due to a current in the first coil is, Again, if self inductance of the first coil or circuit is L_{1}, then, Similarly, coefficient of mutual inductance due to current i

_{2}in the second coil is, Now, if self inductance of the second coil or circuit is, L

_{2}, Now, multiplying (5) and (6), we get, This is an ideal case, when the total changing flux of one coil, links to another coil. The value of M practically not equal to √(L

_{1}L

_{2}) as because the whole flux of one coil does not link with other, rather, a part of the flux of one coil, links with another coil. Hence practically, This k is known as the coefficient of coupling, and this is the ratio of actual coefficient of mutual inductance to ideal (maximum) coefficient of mutual inductance. If the flux of one coil is entirely linked with other, the value of K will be one. This is an ideal case. This is not possible, but when K nearly equal to unity, that means, the maximum flux of one coil links to other, the coils are said to be tightly coupled or closely coupled. But when no flux of one coil links with other, the value of K becomes zero (K = 0), then the coils are said to be very loosely coupled or isolated.

### Mutual Inductance of two Solenoids or Coils

Let us assume two solenoids or coils A and B respectively. Coil A is connected with an alternating voltage source, V. Due to alternating source connected to coil A, it will produce an alternating flux as shown. Now, if we connect on sensitive voltmeter across coil B, we will find a non zero reading on it. That means, some emf is induced in the coil B. This is because, apportion of flux produced by coil A, links with coil B and as the flux changes in respect of time, there will be an induced emf in the coil B according to Faraday’s law of electromagnetic induction. This phenomenon is called mutual induction. That means induction of emf in one coil due to the flux of other coil is mutual induction. Similarly, if the alternating voltage source was connected to coil B and the induced voltage is measured by connecting a voltmeter across coil A, the voltmeter gives a non-zero reading. That means, in this case, the emf will be induced in coil A due to flux linkage from coil B. Let us consider coil A and B have the number of turns N_{1}and N

_{2}. If the entire flux of coil A links with coil B, then weber-turns of the coil B due to unit current of coil A, would be (N

_{2}φ

_{1})/i

_{1}, where, φ

_{1}and i

_{1}is flux and current of coil A. As per definition this is nothing but mutual inductance of coil A and B, M. That is, Similarly, if the current and flux of the coil B are i

_{2}and φ

_{2}.

## Inductances in Series

Let’s coil or inductance A and B are connected in series. The self inductance of coil A, is L_{A}and that of coil B is L

_{B}. Now again consider, M is the mutual inductance between them. There may be two conditions.

- The direction of flux produced by both coil will be in the same direction. In that case, the flux of coil B links will be coil A, will be in the same direction with the flux produced by coil A, itself. Hence, the effective inductance of coil A will be L
_{A}+ M. At the same time, the flux of coil A, links with coil B will be in the same direction with the self-flux of coil B. Hence, the effective inductance of coil B will be L_{B}+ M. Hence total effective inductance of the series connected inductors A and B will be nothing but, - Now, if the direction of instantaneous flux at coil A and B are in opposite, then flux of coil B linking with coil A, will be in opposite direction of flux produced by coil A itself. So, the effective inductance of coil A will be L
_{A}- M. In the same way, the flux of coil A which links with coil B will be in the opposite direction of the self-flux of coil B. Hence, effective inductance of coil B will be, L_{B}- M. So, total inductance in series in this case will be, So, general form of equivalent inductance of two inductors in series in,## Types of Inductor

There are many types of inductors; all differ in size, core material, type of windings, etc. so they are used in wide range of applications. The maximum capacity of the inductor gets specified by the type of core material and the number of turns on the coil. Depending on the value,**inductors**typically exist in two forms, fixed and variable. The number of turns of the fixed coil remains the same. This type is like resistors in shape, and they can be distinguished by the fact that the first color band in a fixed inductor is always silver. They are usually used in electronic equipment as in radios, communication apparatus, electronic testing instruments, etc. The number of turns of the coil in variable inductors, changes depending on the design of the inductor. Some of them are designed to have taps to change the number of turns. The other design is fabricated to have many fixed inductors for which, it can be switched into parallel or series combinations. They often get used in modern electronic equipment. Core or heart of inductor is the main part of the inductor. Some types of inductor depending on the material of the core will be discussed.### Ferromagnetic Core Inductor or Iron-core Inductors

This type uses ferromagnetic materials such as ferrite or iron in manufacturing the inductor for increasing the inductance. Due to the high magnetic permeability of these materials, the inductance can be increased in the response of increasing the magnetic field. At high frequencies, it suffers from core loses, energy loses, that happens in ferromagnetic cores.### Air Core Inductor

The air cored inductor is the type where no solid core exists inside the coil. In addition, the coils that wound on nonmagnetic materials such as ceramic and plastic, are also considered as air cored. This type does not use magnetic materials in its construction. The main advantage of this form of**inductors**is that, at high magnetic field strength, they have a minimal signal loss. On the other hand, they need a bigger number of turns to get the same inductance that the solid cored inductors would produce. They are free of core losses because they do not depend on a solid core.### Toroidal Core Inductor

Toroidal Inductor constructs of a circular ring-formed magnetic core that characterized by it is magnetic with high permeability material like iron powder, for which the wire wounded to get inductor. It works pretty well in AC electronic circuits' application. The advantage of this type is that, due to its symmetry, it has a minimum loss in magnetic flux; therefore it radiates less electromagnetic interference near circuits or devices. Electromagnetic interference is very important in electronics that require high frequency and low power.### Laminated Core Inductor

This form gets typified by its stacks made with thin steel sheets, on top of each other designed to be parallel to the magnetic field covered with insulating paint on the surface; commonly on oxide finish. It aims to block the eddy currents between steel sheets of stacks, so the current keeps flowing through its sheet and minimizing loop area for which it leads to a significant decrease in the loss of energy. Laminated core inductor is also a low-frequency inductor. It is more suitable and used in transformer applications.### Powdered Iron Core

Its core gets constructed by using magnetic materials that get characterized by its distributed air gaps. This gives the advantage to the core to store a high level of energy comparing to other types. Besides, excellent inductance stability is gained with low losses in eddy current and hysteresis. Moreover, it has the lowest cost alternative.## Another Classification of Inductor

### Coupled Inductor

It happens when inductors are related to each other by electromagnetic induction. Generally, it gets used in applications as transformers and where the mutual inductance is required.### RF Inductor

Another name is the radio frequency of RF inductors. This type operates at high-frequency ranges. It is characterized by low current rating and high electrical resistance. However, it suffers from a proximity effect, where the wire resistance increases at high frequencies. Skin effect, where the wire resistance to high frequency is greater than the electrical resistance of current direct.### Multi-Layer Inductor

Here the wounded wire is coiled into layers. By increasing the number of layers, the inductance increases, but with increasing of the capacitance between layers.### Molded Inductor

The material for which it stands from is molded on ceramic or plastic. Molded inductors are typically available in bar and cylindrical shapes with a variety option of windings.### Choke

The main purpose of it is to block high frequencies and pass low frequencies. It exists in two types; RF chokes and power chokes.## Applications of Inductors

In general, there are a lot of applications due to a wide variety of inductors. Here are some of them. Generally, the inductors are very suitable for radio frequency, suppressing noise, signals, isolation and for high power applications. More applications summarized here:- Energy Storage
- Sensors
- Transformers
- Filters
- Motors

**inductor**deviate a little bit from it is real behavior.

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