**Magnetic Circuit:** A magnetic circuit is a closed path that is followed by magnetic field lines of magnetic flux. Materials having high permeability such as soft steel, iron, etc are used in the magnetic circuit. The materials with a high degree of permeability will offer very low resistance to the flow of the magnetic flux.

Let’s consider a coil as shown in the figure below.

There are ‘N’ numbers of turns present in the coil and this coil is wound on a rectangular iron core. As we pass current ‘I’ through the coil, magnetic flux Φ is set up in the iron core. The flux will follow a path ABCDA and the direction of the magnetic flux is given by the “Right-hand thumb rule.”

The magnetic flux Φ depends upon the magnitude of the current ‘I’ and the number of turns ‘N’ of the coil.

The product of ‘N’ and ‘I’ is termed as MMF or magnetomotive force. MMF will determine the amount of flux to be set up in a magnetic circuit.

$m.m.f.=NIAmpereturns$Contents

## Important Terms

We will be discussing the following three terms before proceeding with our further analysis.

### 1. Magnetomotive Force (m.m.f.)

Magnetomotive force is the amount of magnetic pressure which is responsible for setting up the magnetic flux in a magnetic circuit. Mathematically, m.m.f. is the product of the number of turns ‘N’ present in the coil and the current ‘I’ passing through the coil.

$m.m.f.=NIAmpereturns\left(AT\right)$In other words, m.m.f. can be understood as how many times magnetic field lines link up with the current time magnitude of the current.

### 2. Reluctance

Reluctance is the resistance offered to the flow of magnetic flux. This can be thought of as the resistance in an electrical circuit which would offer opposition to the flow of the current.

Reluctance depends upon the physical dimensions such as length and the cross-sectional area. It also depends on the type of material i.e. permeability of the material which would make up the magnetic circuit.

Where ‘l’ is the length, ‘a’ is the cross-sectional area and μ_{r} is the relative permeability and μ_{0} is the permeability of the material in free space.

Magnetic materials such as steel and iron have low reluctance and it is because their relative permeability is high and hence will offer a very low opposition to the flow of magnetic field lines.

### 3. Permeance

Permeance is the measure of the proficiency with which the magnetic field lines (flux) can flow through a circuit.

The permeance can be thought of as analogous to the conductance of an electrical circuit.

## Magnetic Circuit Analysis

For the magnetic circuit analysis let’s consider a circuit consisting of an iron core having a coil with an ‘N’ number of turns. Current ‘I’ is passed through the coil and flux Φ is set up in the core.

The core has a dimension of l meters which is the mean length of the core i.e. the length of WXYZW and cross-sectional area of ‘a’ square meters. Finally, μ_{r} is the relative permeability of the core.

Now, the flux density in the core B is,

The magnetizing force in the material H is,

As the magnetizing force H is equal to the magnetomotive force per unit length ‘l’ and it is expressed as,

The numerator of the above expression is the m.m.f. or the magnetomotive force. And, the denominator term of the above expression is reluctance. So, the above expression of the magnetic flux can be written as,

## Analogy Between Electric Circuit and Magnetic Circuit

The relation of magnetic flux derived in the magnetic circuit analysis shows that magnetic flux is the ratio of m.m.f. and reluctance. From this relationship, we can see a comparableness of the magnetic flux relation to that of Ohm’s Law (I=E/R).

The m.m.f. is comparable to the emf of an electric circuit. Also, the reluctance is analogous to the resistance of the electric circuit and finally, the flux is analogous to the electric current.

The analogy between the electric circuit and the magnetic circuit can be summarized in the table below.

Magnetic Circuit |
Electric Circuit |

M.M.F. |
Voltage or EMF |

Flux |
Current |

Reluctance |
Resistance |

Flux Density |
Current Density |

Magnetic Field Intensity |
No Equivalent Quantity |

## Difference Between Electrical Circuit and Magnetic Circuit

The important difference between the electrical circuit and the magnetic circuit is as follows:

- In a magnetic circuit, there is no energy expended. In simpler words, the energy is required to create the magnetic flux but not to maintain it. But in the case of an electrical circuit, energy is consumed by the circuit as long as the current flows through the circuit which will be dissipated in the form of heat.
- Practically the resistance of an electrical circuit is constant as the resistance depends upon the resistivity and resistivity varies marginally with the temperature rise, however, the reluctance is not a constant quantity. Reluctance depends on the flux density (B).
- In the case of the magnetic circuit, we use Kirchhoff’s flux and MMF Law whereas in the electrical circuit we use Kirchhoff’s Voltage and Current Law.

## Air Gaps in Magnetic Circuit

Small air gaps are present in the magnetic circuit as it becomes a necessity in some practical applications. Such as in the case of an electric motor, a small air gap is present between the rotor and stator to facilitate the mechanical clearance.

The reluctance of the air gap is high, as for the air gap relative permeability μ_{r }is equal to 1.

Here, l_{g} is the length of the air gap and a_{g} is its cross-sectional area.

## Series Magnetic Circuit

In a series magnetic circuit, the same amount of flux Φ flows through each part of the circuit and this is comparable to the series electric circuit where the same amount of current flows through the circuit.

The figure below shows a composite magnetic circuit which is a series circuit that is composed of parts having different dimensions and different materials.

The series of magnetic circuits consist of three different materials along with an air gap. The different materials in the circuit have their own relative permeability. Also, the different parts have their differences in the cross-sectional area and hence the flux density will also be different in all these parts.

The total m.m.f. required to set up a magnetic flux Φ is,

## Parallel Magnetic Circuit

In a parallel magnetic circuit, there is more than one path available for the magnetic field lines (flux) to flow in the circuit. The is comparable to the parallel electrical circuit.

The figure below shows a parallel magnetic circuit.

Here, the coil sets up a total flux Φ in the circuit which gets divided into the parallel paths BE and BCDE.

Consider,

S1 = reluctance of path EFAB

S2 = reluctance of path BE

S3 = reluctance of path BCDE