# Magnetic Circuits: Definition, Concept, Example

## What is Magnetic Circuit?

The closed path followed by the magnetic flux is a magnetic circuit. All electric power machinery such as generators, transformers, and motors depend on their operation on magnetic circuits.

A magnetic circuit consists of a structure composed of most of the 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 field in the core. The magnetic field is in terms of flux lines which form closed loops interlinking with the winding.

According to the basic law of magnetic field i.e Amperes`s 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 basis for the 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.

The 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 the 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

μ0=4π×10-7H/m

in the SI system.

The total flux developed in the circuit is given by:

The above equation is called Ohm`s law for the magnetic circuit sometimes.

## Determination of Ampere-Turns

For the magnetic circuit, the flux created is given by:

## 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 the magnetic circuit,
3. Then, find the number of ampere-turns required for the various parts of the magnetic circuit from the relation AT=Hl, where l is the 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 an air gap is shown in the figure. Air gaps are mainly provided to avoid saturation. An air gap is a volume of air between two magnetic surfaces. The length of the air gap lg equals the distance between the two magnetic surfaces. The area of the 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 a 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 the case of series circuits, all parts of the magnetic circuit carry the same flux, and the 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 are 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 the ampere-turns required to create flux Φ1 in path ABCD are equal to the 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 the magnetic circuit is,

=AT for path DA+AT for path ABCD

=AT for path DA+AT for path AFED