# Magnetic circuits

## Definition

The closed path followed by the magnetic flux is magnetic circuit.All electric power machinery such as generator,transformer,motors depend for their operation on the magnetic circuits.

A magnetic circuit consists of a structure composed for the most of high permeability magnetic material.The core is assumed to be composed of magnetic material whose permeability is much greater than that of the surrounding air.The core is of uniform cross-section and is excited by a winding having N turns and carrying a current of I amperes.This winding develops a magnetic filed in the core.The magnetic filed is in terms of flux lines which form closed loops interlinking with the winding.

Simple Magnetic Circuit

According to basic law of magnetic filed i.e Amperess circuital law ,the line integral of H around a close path is equal to the net current enclosed by that path i.e

This law provides a basic for calculation of magnetic circuits and helps to determine readily the strength of the magnetic field.

## Concepts of Magnetic circuit

The flux produced in the coil on any magnetic circuit is proportional to the number of turns N and the current I .The product of NI is called the Magnetomotive force (mmf) and  helps to determine the amount of flux developed in the magnetic circuit.

Magnetomotive force (mmf) of a magnetic circuit is the magnetic potential difference that tends to force flux around the magnetic circuit and is equivalent to the electromotive force(emf) in an electric circuit.

Reluctance(S):Reluctance represents the opposition of magnetic flux. Reluctance S of the magnetic circuit is directly proportional  to length l, inversely proportional to cross-sectional area a, and dependent on the nature of material of the magnetic circuit.

The reluctance of the magnetic circuit is given by:

Permeability(μ0):When the flux Φ is constant over the length and uniform over the area,the quantity μ expresses the property of the magnetic material called permeability.Permeability is a measure of the receptiveness of the material having magnetic flux developed in it.

For the free space,the permeability

${{\mathbit{\mu }}}_{{\mathbf{0}}}{\mathbf{=}}{\mathbf{4}}{\mathbf{\pi }}{\mathbf{×}}{{\mathbf{10}}}^{\mathbf{–}\mathbf{7}}{\mathbit{H}}{\mathbf{/}}{\mathbit{m}}$

in SI system.

Total flux developed in the circuit is given by:

The above equation is called ohms law for the magnetic circuit sometimes.

## Determination of Ampere-Turns

For the magnetic circuit ,flux created is given by:

## For the determination of Ampere-Turn for a magnetic circuit

1. First of all ,find field strength H in each part of the magnetic circuit,
2. secondly,find the length of various parts of magnetic circuit,
3. Then,find the number of ampere-turns required for the various parts of magnetic circuit from the relation AT=Hl ,where l is length of the parts in meters and
4. Lastly,find the total number of ampere-turns for the whole series magnetic circuit by adding ampere-turns determined for various paths in magnetic circuits.

## Magnetic circuits with Air Gaps

A magnetic circuit with air gap is shown in the figure.Air gaps are mainly provided to avoid the saturation.An air gap is a volume of air between two magnetic surfaces.The length of air gap lg equals the distance between the two magnetic surfaces.The area of x-section of any one of the surfaces gives the air-gap area,ag. when the air gap length lg is much smaller than the dimensions of the adjacent core faces,the magnetic flux Φ is constrained essentially to reside in the core and the air gap and is continuous throughout the magnetic circuit.

since the permeability of air is constant,the air gap is linear part of the magnetic circuit and the flux density in the air gap is proportional to the mmf across the air gap.The mmf is calculated separately for the air gap and the iron portions and then added to determine the total mmf.

## Composite magnetic circuits

consider a circular ring made from different materials of lengths l1,l2 and l3 ,cross-sectional areas a1,a2 and a3 and relative permeability μr1,μr2 and μr3 respectively with a cut of length lg called air gap.The total reluctance is the arithmetic sum of individual reluctance as they are joined in series.

## Parallel magnetic circuits

In case of series circuits,all parts of the magnetic circuit carry same flux and total ampere-turns required to create a given flux is the arithmetic sum of the ampere-turns required for individual parts of the circuit.

But for the magnetic circuit in parallel ,the ampere turns required for the combination is equal to the ampere-turns required to create the given flux in one path.

From the given circuit above,

ABCD and AFED are in parallel ,so ampere-turns required to create flux Φ1 in path ABCD is equal to ampere-turns required to create flux Φ1 in path AFED and also equal to the ampere-turns required for both of the paths.

Hence total ampere-turns required for magnetic circuit is,

=AT for path DA+AT for path ABCD

=AT for path DA+AT for path AFED