# Series Magnetic Circuit

**Definition:** The **Series Magnetic Circuit** is defined as the magnetic circuit having number of parts of different dimensions and materials carrying the same magnetic field.

Consider a circular coil or solenoid having different dimensions as shown in the figure below

Current I is passed through the solenoid having N number of turns wound on the one section of the circular coil. Φ is the flux, sets up in the core of the coil.

a_{1}, a_{2}, a_{3} are the cross-sectional area of the solenoid.

*l _{1}, l_{2}, l_{3} are* the length of the three different coils having different dimension joined together in series.

µr_{1}, µr_{2}, µr_{3 }are the relative permeability of the material of the circular coil.

a_{g }and are the area and the length of the air gap.

The total reluctance (S) of the magnetic circuit is

Total mmf = φ x S ……..…. (1)

Putting the value of S in equation (1) we get

(As B = φ/a) putting the valve of B in the equation (2) we obtain the following equation for the total MMF

Procedure for the Calculation of the total MMF for the Series Magnetic Circuit

- The magnetic circuit is divided into different section or parts.
- Now determine the value of the flux density (B) of the different sections. As we know B = φ/a where φ is the flux in Weber, and a is the area of cross-section in m
^{2} - Determine the value of the magnetising force (H) as we know that H = B/µ
_{0}µ_{r }where B is the flux density in Weber/ m^{2}and µ_{0}is absolute permeability and its value is 4πx10^{-7}, and µ_{r }is the relative permeability of the material, and its value will be given. If the value of µ_{r}is not given, then you have to compute the value from the value of H from the**B-H curve** - The value of magnetizing force (H) as H
_{1,}H_{2}, H_{3}, Hg will be individually multiplied by the length of the different sections that is ,*l*and_{1}, l_{2}, l_{3}*lg*respectively.

- Finally, add all the values of Hx
**l**

**The value of H for the air gap part will always µ _{g} = B/µ_{0.}**

**B-H Curve**

The graph plotted between the flux density (B) and the magnetizing force (H) of any material is called B-H Curve or the magnetization curve.

The shape of the B-H curve is mostly non-linear this means that the relative permeability (µ_{r}) of the material varies and is not constant. The value of relative permeability mainly depends on the value of flux density. But for the non-magnetic materials like plastic, rubber, etc. and for magnetic circuit having air gap its value is constant, denoted by (µ_{0}). Its value is 4πx10^{-7 }H/m and commonly known as absolute permeability or permeability of free space.

B-H curve for the various material like cast iron, cast steel and sheet steel is shown below.