Determine the shunt field current in a magnetic circuit

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Discussion Overview

The discussion revolves around determining the shunt field current in a magnetic circuit, focusing on the assumptions regarding cross-sectional areas and the implications of these assumptions on magnetic flux density. Participants explore theoretical aspects and practical considerations related to magnetic circuits.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant attempts to solve the problem by calculating flux density, permeability, and reluctance but encounters difficulties.
  • Another participant presents their solution but expresses uncertainty about its correctness and seeks confirmation.
  • Confusion arises regarding the assumption that the cross-sectional areas of the left and right branches of the toroidal core are the same as the air gaps, with one participant questioning this assumption.
  • A participant suggests that the cross-section is uniform throughout the magnetic path, despite the drawing suggesting otherwise.
  • Another participant agrees with the notion that the "path" should reflect the indicated area, proposing that the pole area should be considered as double the indicated area.
  • Two cases are presented: one where the area is uniform throughout the magnetic path and another where the pole area is twice that of the branches, discussing the implications for magnetic flux density and practical applications.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions regarding cross-sectional areas and their effects on magnetic flux density, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

Participants note limitations in the assumptions made about the uniformity of the magnetic path and the characteristics of the BH curve, which remain unresolved.

Fatima Hasan
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Homework Statement
Written below.
Relevant Equations
Equations are attached below.
Problem Statement :
Problem-Statement.png


Here's my attempt :
* By assuming that the fringing and leakage effects are ignored.
Solution.gif


I find the flux density , the permeability and the reluctance of the iron , but then I get stuck .
Any help would be greatly appreciated .
 

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    Equations.gif
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I tried to solve it , and that's what I got :
Analog Circuit :

Analog Circuit.JPG


02*89577.47154%20%5C%5C%5C%5Ci%3D1.49%5Capprox%201.gif


That's what I got , but I am not sure if my answer is correct or not .
I want to confirm my answer .
 
The statement states that the flux path has a net cross-sectional area of 200 cm^2.
Based on this statement, I am a bit confused about the assumption that the cross-sectional area of left branch and right branch of the toroidal core are the same as the cross-sectional area of the air gaps.
 
Last edited:
alan123hk said:
The statement states that the flux path has a net cross-sectional area of 200 cm^2.
Based on this statement, I am a bit confused about the assumption that the cross-sectional area of left branch and right branch of the toroidal core are the same as the cross-sectional area of the air gaps.
Yes it's not given. So I would assume the cross-section is uniform thruout the magnetic path, the drawing strongly suggesting otherwise notwithstanding.
 
I agree with alan123hk: the "path" has to be the area for indicated path. That means the pole area has to be double=400 cm^2
Then n*I=Hfe*Lfe+B/μo*2*airgaplengs [n=number of turns]
 
Case 1 : the area is uniform throughout the magnetic path
Case 2 : the area of the pole is twice that of the left/right branch

Assume that the entire magnetic circuit has the same BH curve characteristics

In case 1, the B in the pole is twice that of the B in the left/right branch, and since the pole becomes bottleneck, the maximum magnetic flux density in the left/right branch may not be fully utilized.

In case 2, the entire magnetic circuit has the same B everywhere, there is no bottleneck, and the maximum magnetic flux density can be achieved throughout the entire magnetic circuit.

Of course, if uniform magnetic flux density is not the primary concern, then case 1 is still the choice in practical applications, since there may be many other factors to be considered, such as mechanical strength and reducing eddy current/hysteresis loss.
 
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