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

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

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.

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

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

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 Hysteresis

21/01/ Hysteresis

21/01/ Hysteresis

21/01/ Hysteresis

21/01/ Hysteresis

21/01/ 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 are aligned, forming very small bar magnets. 21/01/ 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. 21/01/ Hysteresis

21/01/ Ampere’s Circuital Law – KVL

21/01/ Ampere’s Circuital Law – (KVL)

21/01/ The Flux Φ – (KCL)

 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/ Series Magnetic Circuits

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

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

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/ Series Magnetic Circuits

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

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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