1. Lecture 4 by Moeen Ghiyas Chapter 11 – Magnetic Circuits 21/01/20161

2. TODAY’S LECTURE CONTENTS  Review Ohm’s Law For Magnetic Circuits Magnetizing Force  Hysteresis  Ampere’s Circuital Law – (Applying KVL)  The Flux Φ – (Applying KCL)  Series Magnetic Circuits

3. Ohm’s Law For Magnetic Circuits  Ohm’s law for magnetic circuit  Where the magnetomotive force F is proportional to the product of the number of turns N around the core (in which the flux is to be established) and the current I through the turns of wire  Obviously, an increase in the number of turns N or the current I through the wire will result in an increased “pressure” on the system to establish flux lines through the core.

4. Magnetizing Force  The magneto-motive force per unit length is called the magnetizing force (H). In equation form,  But from Ohm’s law for magnetic circuits, we know  Substituting above, we have 21/01/20164

5. Magnetizing Force  The applied magnetizing force has a pronounced effect on the resulting permeability of a magnetic material. 21/01/20165

6. Magnetizing Force  Also the flux density and the magnetizing force are related by the following equation:  This equation indicates that for a particular magnetizing force, the greater the permeability, the greater will be the induced flux density. 21/01/20166

7. 7 Hysteresis

8. 21/01/2016 8 Hysteresis

9. 21/01/2016 9 Hysteresis

10. 21/01/2016 10 Hysteresis

11. 21/01/2016 11 Hysteresis

12. 21/01/2016 12 Hysteresis

13.  Domain Theory of Magnetism  The atom, due to its spinning electrons, has magnetic field associated.  In nonmagnetic materials, the net magnetic field is zero since the magnetic fields due to the atoms oppose each other.  In magnetic materials such as iron and steel, however, the magnetic fields of groups of atoms in the order of 10 12 are aligned, forming very small bar magnets. 21/01/2016 13 Hysteresis

14.  Domain Theory of Magnetism  This group of magnetically aligned atoms is called a domain.  Each domain is a separate entity; that is, each domain is independent of the surrounding domains.  For an un-magnetized sample of magnetic material, these domains appear in a random manner, such as shown in fig.  The net magnetic field in any one direction is zero. 21/01/2016 14 Hysteresis

15. 21/01/2016 15 Ampere’s Circuital Law – KVL

16. 21/01/2016 16 Ampere’s Circuital Law – (KVL)

17. 21/01/2016 17 The Flux Φ – (KCL)

18.  Magnetic circuit problems are basically of two types:  In one type, Φ is given, and the impressed mmf NI must be computed (problem encountered in the design of motors, generators, and transformers).  In the other type, NI is given, and the flux Φ of magnetic circuit must be found (problem encountered primarily in the design of magnetic amplifiers and is more difficult since the approach is “hit or miss.”  For magnetic circuits, the level of B or H is determined from using the B-H curve. 21/01/2016 18 Series Magnetic Circuits

19.  Ex ample – For the series magnetic circuit of fig: a) Find the value of I required to develop a magnetic flux of Φ = 4 x 10 -4 Wb. b) Determine μ and μ r for the material under these conditions. 21/01/2016 19 Series Magnetic Circuits

20. a) Find the value of I required to develop a magnetic flux Φ = 4 x 10 -4 Wb  Solution 21/01/2016 20 Series Magnetic Circuits

21. a) Find the value of I required to develop a magnetic flux Φ = 4 x 10 4 Wb  Solution  Using B – H curves of fig, we can determine magnetizing force H: . H = 170 At / m 21/01/2016 21 Series Magnetic Circuits

22. b) Determine μ and μ r for the material under these conditions. 21/01/2016 22 Series Magnetic Circuits

23. Summary / Conclusion  Review Ohm’s Law For Magnetic Circuits Magnetizing Force  Hysteresis  Ampere’s Circuital Law – (Applying KVL)  The Flux Φ – (Applying KCL)  Series Magnetic Circuits

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