Basic Electronics - Inductance

# Basic Electronics – Inductance

The property of an inductor to get the voltage induced by the change of current flow, is defined as Inductance. Inductance is the ratio of voltage to the rate of change of current.

The rate of change of current produces change in the magnetic field, which induces an EMF in opposite direction to the voltage source. This property of induction of EMF is called as theÂ Inductance.

The formula for inductance is

Inductance=volatgerateofchangeofcurrent

Units âˆ’

• The unit of Inductance isÂ Henry. It is indicated byÂ L.
• The inductors are mostly available in mHÂ milliHenryÂ and Î¼HÂ microHenry.

A coil is said to have an inductance ofÂ one HenryÂ when an EMF ofÂ one voltÂ is self-induced in the coil where the current flowing changed at a rate ofÂ one ampere per second.

### Self-Inductance

If a coil is considered in which some current flows, it has some magnetic field, perpendicular to the current flow. When this current keeps on varying, the magnetic field also changes and this changing magnetic field, induces an EMF, opposite to the source voltage. This opposing EMF produced is theÂ self-induced voltageÂ and this method is called asÂ self-inductance.

The currentÂ isÂ in the figure indicate the source current whileÂ iindÂ indicates the induced current. The flux represents the magnetic flux created around the coil. With the application of voltage, the currentÂ isÂ flows and flux gets created. When the currentÂ isÂ varies, the flux gets varied producingÂ iind.

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

We can write the above equation as

EÎ±dIdt

E=LdIdt

Where,

• EÂ is the EMF produced
• dI/dtÂ indicates the rate of change of current
• LÂ indicates the co-efficient of inductance.

Self-inductance or Co-efficient of Self-inductance can be termed as

L=EdIdt

The actual equation is written as

E=âˆ’LdIdt

The minus in the above equation indicates thatÂ the EMF is induced in opposite direction to the voltage sourceÂ according to Lenzâ€™s law.

### Mutual Inductance

As the 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 region of the primary, then the varying magnetic flux induces an EMF in the second coil. If this first coil is called asÂ Primary coil, the second one can be called as aÂ Secondary coil.

When the EMF is induced in the secondary coil due to the varying magnetic field of the primary coil, then such phenomenon is called as theÂ Mutual Inductance.

The currentÂ isÂ in the figure indicate the source current whileÂ iindÂ indicates the induced current. The flux represents the magnetic flux created around the coil. This spreads to the secondary coil also.

With the application of voltage, the currentÂ isÂ flows and flux gets created. When the currentÂ isÂ varies, the flux gets varied producingÂ iindÂ in the secondary coil, due to the Mutual inductance property.

The change took place like this.

VpIpâ†’Bâ†’VsIs

Where,

• VpÂ ipÂ Indicate the Voltage and current in Primary coil respectively
• BÂ Indicates Magnetic flux
• VsÂ isÂ Indicate the Voltage and current in Secondary coil respectively

Mutual inductanceÂ MÂ of the two circuits describes the amount of the voltage in the secondary induced by the changes in the current of the primary.

V(Secondary)=âˆ’MÎ”IÎ”t

WhereÂ Î”IÎ”tÂ the rate of change of current with time andÂ MÂ is the co-efficient of Mutual inductance. The minus sign indicates the direction of current being opposite to the source.

Units âˆ’

The units of Mutual inductance is

volt=Mampssec

Fromtheaboveequation

M=volt.secamp

=Henry(H)

Depending upon the number of turns of the primary and the secondary coils, the magnetic flux linkage and the amount of induced EMF varies. The number of turns in primary is denoted by N1 and secondary by N2. The co-efficient of coupling is the term that specifies the mutual inductance of the 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 more, the inductance offered by that inductor gets less and vice versa.

### Cross sectional area of the coil

The cross sectional area of the coil is directly proportional to the inductance of the coil. The higher the area of the coil, the higher the inductance will be.

### Number of turns

With the number of turns, the coil affects the inductance directly. The value of inductance gets square to the number of turns the coil has. Hence the higher the number of turns, square of it will be the value of inductance of the coil.

### Permeability of the core

TheÂ permeabilityÂ Î¼Â of the core material of inductor indicates the support the core provides for the formation of a magnetic field within itself. TheÂ higherÂ the permeability of the core material, theÂ higherÂ will be the inductance.

## Coefficient of Coupling

This is an important factor to be known for calculating Mutual inductance of two coils. Let us consider two nearby coils of N1 and N2 turns respectively.

The current through first coil i1Â produces some flux Î¨1. The amount of magnetic flux linkages is understood by weber-turns.

Let the amount of magnetic flux linkage to the second coil, due to unit current of i1Â be

N2Ï†1i1

This can be understood as the Co-efficient of Mutual inductance, which means

M=N2Ï†1i1

Hence the Co-efficient of Mutual inductance between two coils or circuits is understood as the weber-turns in one coil due to 1A of current in the other coil.

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

L1i1=N1Ï†1=>L1N1Ï†1i1

M=N2L1N1

Similarly, coefficient of mutual inductance due to current i2Â in the second coil is

M=N1Ï†2i2â‹¯â‹¯â‹¯â‹¯1

If self-inductance of second coil is L2

L2i2=N2Ï†2

L2N2=Ï†2i2

Therefore,

M=N1L2N2â‹¯â‹¯â‹¯â‹¯2

Multiplying 1 and 2, we get

MÃ—M=N2L1N1Ã—N1L2N2

M2=L1L2=>M=L1L2

The above equation holds true when the whole changing flux of primary coil links with the secondary coil, which is an ideal case. But in practice, it is not the case. Hence, we can write as

Mâ‰ L1L2

andML1L2=Kâ‰ 1

Where K is known as the coefficient of coupling.

TheÂ Coefficient of coupling KÂ can be defined as the ratio of actual coefficient of mutual inductance to the idealÂ maximumÂ coefficient of mutual inductance.

If the value of k is near 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

There are many applications of Inductors, such as âˆ’

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