# Specifications of Inductor: (With mathematical expressions)

Different specifications of Inductor | Inductance of coil | Inductive reactance | self- inductance | Mutual inductance | Mathematical equation |

## Specifications of Inductor:

When we working with an inductor we must very well know about all specifications of the inductor they are as;

1. The inductance of coil 2. Inductive reactance 3. Self-inductance 4. Mutual inductance.

### 1. Inductance of coil:

Inductance is the property of an electric circuit whereby changes in the current flowing through it produces changes in the magnetic field. Its unit is Henry (H).

The figure shows the basic construction of an inductor coil. In the construction of an inductor coil, copper wire has used and this copper wire is wound on the iron core. The inductances of the coil depend on the following factors:

• If the number of turns is greater then inductance increases because more voltage can be induced.
• If the area of each turn increases then the value of the inductance again increases.
• Inductance increase with permeability (µ) of the core.
• If the length of same number of turns increases then the value of inductance decreases.
• The inductance for the single coil can be calculated by using following formula;

∴ L = ( µ N2A ) / l

Whereas,

L= inductance of coil in henry

N=number of turns of coils

A=area of the coil in square-meter

L=length of core in meter

µ=permeability of medium

µ=µ0 µr

µ0=Absolute permeability

µr=Relative permeability

### 2. Inductive reactance:

According to Lenz’s law, a changing inductor current induces a voltage across an inductor in a direction that opposes the change in current. When an ac sinusoidal current applied to an inductor, a voltage will induce in a direction to always oppose the change in ac current.

This opposition to the change in AC current in an inductor is similar to the opposition to dc current in a resistance element. This resistance to the change in the ac inductor current is called inductive reactance (XL) and is measured in ohms.

The equation for inductive eactance is given as;

∴ XL = ωL = 2 . ∏ . F . L

Whereas,

F=frequency in hertz (Hz)

L=inductance in henry (H)

XL=Inductive reactance in Ω

From the above equation, the inductive reactance (XL) of the inductor is directly proportional to frequency and inductance.

Thus for low frequency, the inductive reactance of the inductor is also, if inductance (L) is Constance, then inductor less opposes to any change in the current flowing through it.

For high frequency, the inductive reactance of inductor is also high, if inductance (L) is constant then inductor more oppose to any change in the current flowing through it.

### 3. Self-Inductance:

We know that according to the lenz’s law, the direction of the self-induced E.M.F is such that it produce a current which opposes the cause producing the E.M.F itself.

Here the cause behind, the production of self-induced E.M.F is the change in current through the coil. Hence the induced voltage will try to oppose any change in coil current.

In other words, the self -induced E.M.F will try to maintain the coil current constant. If the coil current is increased by reducing R then the self-induced voltage will try to reduce this increased current back to its original value.

And if the coil current is reduced by increasing “R” then the self-induced voltage will try to increase this current back to its original value.

Thus the coils oppose any change in current through it. This property of the coil to oppose any change in the current flowing through it which known as the self-inductance.

Expression for coefficient of self-induction (L):

It will define as flux linkage per ampere current in it. Its unit is Henry (H).

∴ L = N Φ / I

Whereas,

N= No. of turns

Φ= Magnetic flux

I= Current

But Φ = m.mf/Reluctance = NI/S

∴ L = (N . NI ) / I .s

L = N2/ s Henries.

### 4. Mutual inductance:

Mutual inductance defined as the property due to which the change in current through one coil produces an E.M.F in the other coil placed nearby, by induction. It has denoted by “M” and measured in Henry (H).

The coefficient of the mutual inductance defined as the property of E.M.F which gets induced into the second coil because of a change in the current flowing through the first coil. It will measure in Henries.

∴ M = N2 Φ 2 /I1

Whereas,

N2=No. of turns of the second coil.

Φ 2= Magnetic flux of the second coil

I2= Current in the first coil

The Φ2 is the part of the flux Φ1 produced due to L1. Let k1 be the fraction of Φ1 which is linking with the second coil.

Φ 2= k1. Φ 1

M = (N2. k1. Φ1) / I1

### 5. Special specifications of inductor:

• Coefficient of coupling.
• Q- factor or Quality factor of an inductor.

Electromagnetic induction