Series Magnetic Circuit

05/28/2025

Definition of Series Magnetic Circuit

Definition: A series magnetic circuit is defined as a magnetic pathway composed of multiple sections with varying dimensions and materials, all carrying the same magnetic field. Consider a circular coil or solenoid with distinct dimensional parameters, as illustrated in the figure below:

Series Magnetic Circuit Analysis

A current I flows through a solenoid with N turns wound around one section of a circular coil, inducing a flux Φ in the core.

a₁, a₂, a₃: Cross-sectional areas of the solenoid sections
l₁, l₂, l₃: Lengths of the three serially connected coil sections with different dimensions
μᵣ₁, μᵣ₂, μᵣ₃: Relative permeabilities of the circular coil materials
a₉, l₉: Area and length of the air gap (assuming ag denotes air gap area)

The total reluctance (S) of the magnetic circuit is:

Procedure for Calculating Total MMF in Series Magnetic Circuits

- Sectionalize the magnetic circuit into distinct parts.
- Determine flux density (B) for each section using $B =ϕ/a$ , where $ϕ$ is flux (Weber) and $a$ is cross-sectional area (m²).
- Calculate magnetizing force (H) using H=B/(μ0μr), where:
  - $B$ is flux density (Wb/m²),
  - $μ_{0} = 4 π \times 1 0^{-7}$ (absolute permeability),
  - μr is relative permeability (provided or derived from the B-H curve if unknown).
- Multiply each H value(e.g., $H1, H2, H3, Hg$ ) by the corresponding section length ( $l1, l2, l3, lg$ ).
- Sum all products of H×l to obtain the total MMF:Total MMF $= H 1 l 1 + H 2 l 2 + H 3 l 3 + H g l g)$

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

Topics

Basic Circuit Theory Circuit Analysis

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