Total reluctance in a magnetic core

[kevinb]

Homework Statement

I am looking for a general explanation of when the total reluctance of a magnetic circuit is not equivalent to the sum of the reluctances if each area. In several examples the text has added 2 areas in parallel and then added the third area. I'm not 100% sure on when this is required.

Homework Equations

I use R=l/(μA) to determine the reluctance of each area, but don't know if/when reluctances need to be added in parallel.

The Attempt at a Solution

For example, if I have a shape like this:

where the shaded region is air and the rest (the white area) is iron, I calculated the reluctance for the left, middle, right and small air gap. However, is the total the simple addition of them or are the left and right "legs" in parallel?

 

[Astronuc]

The center is in series with the two outer loops which are in parallel.

See page 11 of 35 in http://www.ece.msstate.edu/~donohoe/ece3183magnetic_circuits_and_transformers.pdf

or page 29 of 33 in http://www1.mmu.edu.my/~wslim/lecture_notes/Chapter4.pdf

It's a fairly standard magnetic circuit. One must treat the air gap as well.

 

[kevinb]

Thank you very much. Those two documents were perfect explanations for this particular circuit, but I'll read them further so I gain a better grasp of the general principles as well.