1. Chapter 11 – Magnetic Circuits Lecture 6 by Moeen Ghiyas 24/05/2016 1

2. Review Ampere’s Circuital Law – (Applying KVL) The Flux Φ – (Applying KCL) Air Gaps Series-Parallel Magnetic Circuits Determining Flux Φ

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5. The spreading of the flux lines outside the common area of the core for the air gap in fig (a) is known as fringing. Neglect this effect of fringing as shown in fig (b) The flux density of air gap is given by Where, 24/05/2016 5

6. For most practical applications, the permeability of air is taken to be equal to that of free space. The magnetizing force of the air gap is then determined by and the mmf drop across the air gap is equal to H g l g. An equation for H g is as follows: 24/05/2016 6

7. Example – Find the value of I required to establish a magnetic flux of φ = 0.75 x 10 -4 Wb in the series magnetic circuit of fig Solution 24/05/2016 7

8. Example – Find the value of I, φ = 0.75 x 10 -4 Wb Solution 24/05/2016 8

9. Example – Determine the current I required to establish a flux of φ =1.5 x 10 -4 Wb in the section of the core indicated in fig Solution 24/05/2016 9

10. Example – Determine the current I required to establish a flux of φ =1.5 x 10 -4 Wb in the section of the core indicated in fig Solution 24/05/2016 10

11. Example – Determine the current I required to establish a flux of φ =1.5 x 10 -4 Wb in the section of the core indicated in fig Solution 24/05/2016 11

12. Example – Determine the current I required to establish a flux of φ =1.5 x 10 -4 Wb in the section of the core indicated in fig Solution 24/05/2016 12

13. Example – Determine the current I required to establish a flux of φ =1.5 x 10 -4 Wb in the section of the core indicated in fig Solution 24/05/2016 13

14. To demonstrate that µ is sensitive to the magnetizing force H, the permeability of each section is determined For section bcde, For section be, For section efab, 24/05/2016 14

15. Here NI is given and the flux φ must be found. This is a relatively straightforward problem if only one magnetic section is involved. Then For magnetic circuits with more than one section, there is no set order of steps that will lead to an exact solution for every problem on the first attempt. 24/05/2016 15

16. We must find the impressed mmf for a calculated guess of flux φ and then compare this with specified value of mmf. For most applications, a value within ±5% of the actual Φ or specified NI is acceptable. We can make a reasonable guess at the value of Φ if we realize that the maximum mmf drop appears across the material with the smallest permeability if the length and area of each material are the same. 24/05/2016 16

17. Example – Calculate the magnetic flux Φ for the magnetic circuit of fig Solution 24/05/2016 17

18. Example – Find the magnetic flux Φ for the series magnetic circuit of fig for the specified impressed mmf. Solution 24/05/2016 18

19. Example – Find the magnetic flux Φ Solution 24/05/2016 19

20. Example – Find the magnetic flux Φ Solution 24/05/2016 20

21. Example – Find the magnetic flux Φ Solution 24/05/2016 21

22. Review Ampere’s Circuital Law – (Applying KVL) The Flux Φ – (Applying KCL) Series Magnetic Circuits Air Gaps Series-Parallel Magnetic Circuits Determining Flux Φ Applications

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