Inductor | inductance | Units | Formula

What is Inductor

Inductor is a passive two terminal electrical component that stores energy in the form of magnetic field when current passes through it. It consists a insulated wire wound on magnetic core made of ferromagnetic material. The inductor is denoted by letter “L”. The inductor is also called a choke, reactor or just coil. The symbol of inductor is given below

What is Inductance

It is the property of inductor by which energy is stored in a inductor in the form of magnetic field. The significant and distinguishing feature of inductance is that it makes itself felt in a circuit only, when there is a changing current. The SI unit of inductance is henry, denoted by letter “L”.

The various formulae for inductance can be derived from circuit viewpoint, Geometrical viewpoint and Energy viewpoint

Circuit Viewpoint

Consider the circuit shown below \\\;\\\;\;\;V_{L}=L\frac{di}{dt}\;\;\;\;\;\;\;\;\;\;(1)\\\;\\ According to equation (1) The potential difference across the terminals of inductor appears when there is changing current.

For Direct Current \\\;\\\;\;\;\frac{di}{dt}=0\\\;\\then \\\;\\ V_{L}=L\frac{di}{dt}=L(0)=0\\Thus for Direct Current (DC) inductor behaves as a short circuit.

Graphical representation of inductor from circuit viewpoint are shown below.

Energy Viewpoint

Let “i” is the current in the circuit and “V_L ” is the potential difference between the inductor of inductance “L” as shown in above figure.\\Energy Stored in the inductor between the time interval of “0” to “t” is \\\;\\E=\int_{0}^{t}V_{L}idt\;\;\;\;\;\;\;\;(2)

Putting the Value of “V_L ” from equation (1) into equation (2)\\\;\\E=\int_{0}^{t}(L\frac{di}{dt})idt

E=L\int_{0}^{t}idi\\\;\\E=\frac{1}{2}Li^{2}\;\;\;\;\;\;\;(3)

Geometrical Viewpoint

Consider a inductor having “N” number of turns, Length “l” , Area of cross section “A” and core of material having permeability “\mu“. Let “i” is the current in the inductor of inductance “L”.

Total Flux (N\phi) is directly proportional to the current (i) i.e.\\\;\\N\phi \propto i\\\;\\N\phi = L i\\\;\\L = \frac{N\phi}{i}\;\;\;\;\;\;\;(4)\\

we know \\\;\\\phi=\frac{mmf}{Magnetic\;reluctance}=\frac{Ni}{r}\;\;\;\;\;\;\;(5)\\\;\\Magnetic reluctance, r = \frac{l}{\mu A}

Putting The value of magnetic reluctance (r) in equation (5), Thus \\\;\\\phi=\frac{Ni\mu A}{L}

Putting the value of “\phi” in equation (4). Thus\\\;\\L=\frac{N^2 \mu A}{l}

Types of Inductors

The inductors are classified on the basis of material used in the core. The various types of inductors are

1. Air Core Inductor
2. Iron Core Inductor
3. Iron Powder Inductor
4. Ferrite Core Inductor

Air Core inductor: These are inductors the core material is plastic, ceramic, or other nonmagnetic materials, or have only air inside the windings (i.e.Turns). They provide low inductance than iron core inductors. They are generally more effective at high frequencies and don’t suffer as much core loss. They have  high-Quality factor.

Iron Core Inductor: These are inductors which use  Ferromagnetic materials such as Iron or ferrite as a core material. They have high power and high inductance. However, they are limited in high-frequency capacity. These inductors are used in audio equipment, Industrial power supplies, Power conditioning, Inverter systems etc.

Iron Powder Inductor: The cores of these inductors are made of highly pure iron powder (100%). It gives us a solid looking core when this iron power is compressed under very high pressure and mixed with a binder such as epoxy or phenolic. By this action iron powder forms like a magnetic solid structure which consists of distributed air gaps. These inductors are capable to store high magnetic flux. These inductors posses high temperature co-efficient stability. These are mainly applicable in switching power supplies. These inductors are commonly used in power conversion, line filter applications and radio frequency applications.

Ferrite Core Inductor: The cores of these inductors are made of ferromagnetic material. The ferromagnetic material is mixture of metal oxide of iron and other elements to form crystalline structures. The general composition of ferrites is XFe₂O₄ where “X” represents transition materials. Mostly the transition materials used are  manganese and zinc (MnZn), nickel and zinc (niZn). These ferrites are divided into – soft ferrites and hard ferrites.

\;\;\;\;\;soft ferrites: These are the Materials that have the ability to reverse their polarity without any external energy.\\\;\;\;\;\;Hard Ferrite: These are also called as permanent magnets. These will keep the polarity of the magnetization even after removing the magnetic field. They are not used in inductors because of their high hysteresis loss

Ferrite core inductor will help to improve the performance of the inductor by increasing the permeability of the coil which leads to increase the value of the inductance. The level of the permeability of the ferrite core used within the inductors will depend on the ferrite material. This permeability level ranges from 20 to 15,000 according to the material of ferrite. Thus the inductance is very high with ferrite core when compared to the inductor with air core.

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