ELECTRIC CIRCUIT ANALYSIS - I

1. Lecture 4 by MoeenGhiyas Chapter 11 – Magnetic Circuits ELECTRIC CIRCUIT ANALYSIS - I

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 Fis 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

5. Magnetizing Force • The applied magnetizing force has a pronounced effect on the resulting permeability of a magnetic material.

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.

7. Hysteresis

8. Hysteresis

9. Hysteresis

10. Hysteresis

11. Hysteresis

12. Hysteresis

13. Hysteresis • 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 1012 are aligned, forming very small bar magnets.

14. Hysteresis • 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.

15. Ampere’s Circuital Law – KVL

16. Ampere’s Circuital Law – (KVL)

17. The Flux Φ – (KCL)

18. Series Magnetic Circuits • 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.

19. Series Magnetic Circuits • Ex ample – For the series magnetic circuit of fig: • Find the value of I required to develop a magnetic flux of Φ = 4 x 10-4Wb. • Determine μ and μr for the material under these conditions.

20. Series Magnetic Circuits • Find the value of I required to develop a magnetic flux Φ = 4 x 10-4 Wb • Solution

21. Series Magnetic Circuits • Find the value of I required to develop a magnetic flux Φ = 4 x 104Wb • Solution • Using B – H curves of fig, we can determine magnetizing force H: • . H = 170 At / m

22. Series Magnetic Circuits • Determine μ and μr for the material under these conditions.

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