BASIC ELECTRICAL ENGINEERING D. C. KULSHRESHTHA, PowerPoint Slides PROPRIETARY MATERIAL. © 2010 The McGraw-Hill Companies, Inc. All rights reserved. No part of this PowerPoint slide may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this PowerPoint slide, you are using it without permission. Next Chapter 6 Magnetic Circuits D.C. Kulshreshtha Next Thought of the DAY There are no secrets to success. It is the result of preparation, hard work, and learning from failure. --Colin Powell.. Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 3 Topics to be Discussed Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance (R). Analogy between Electric and Magnetic Circuits. Composite Magnetic Circuit. Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 4 Introduction Unlike electric field lines, the lines of magnetic flux form closed loops. A magnetic circuit is a closed path followed by lines of magnetic flux. A copper wire, because of its high conductivity, confines the electric current within itself. Similarly, a ferromagnetic material (such as iron or steel), due to its high permeability, confines magnetic flux within itself. Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 5 Magnetomotive Force (MMF) The electric current is due to the existence of an electromotive force (emf). By analogy, we may say that in a magnetic circuit, the magnetic flux is due to the existence of a magnetomotive force (mmf). mmf is caused by a current flowing through one or more turns. The value of the mmf is proportional to the current and the number of turns. It is expressed in ampere turns (At). But for the purpose of dimensional analysis, it is expressed in amperes. Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 6 Magnetic Field Strength (H) The mmf per metre length of the magnetic circuit is termed as the magnetic field strength, magnetic field intensity, or magnetizing force. It units are ampere-turns per metre (At/m) . Its value is independent of the medium . F IN H l l Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 7 Magnetic Permeability (μ) If the core of the toroid is vacuum or air, the magnetic flux density B in the core bears a definite ratio to the magnetic field strength H. This ratio is called permeability of free space. Thus, for vacuum or air, B 7 0 4 10 Tm/A H Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 8 The flux produced by the given mmf is greatly increased, if iron replaces the air in the core. As a result, the flux density B also increases many times. In general, we can write B = μH. μ is called the permeability of the material. Normally, we write μ = μr μ0. μr is called relative permeability (just a number). Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 9 Reluctance (R) and Permeance (G) The current in an electric circuit is limited by the presence of resistance of the electric circuit. Similarly, the flux Φ in a magnetic circuit is limited by the presence of the reluctance of the magnetic circuit, 1 l 1 l R A r 0 A The reciprocal of reluctance is known as permeance (G). Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 10 Magnetic Circuit Theory For a toroid, mmf, F = NI ampere-turns. Because of this mmf, a magnetic field of strength H is set up throughout the length l. Therefore, F = Hl If, B is the flux density, total flux is given as Φ=BA Dividing, we get Click F Φ BA B A A A r 0 Φ l /(r 0 A) F Hl H l l l Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 11 E I R Comparing this with 1 l We get R r 0 A Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 12 Analogy between Electric and Magnetic Circuits Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 13 Example 1 Calculate the magnetomotive force (mmf) required to produce a flux of 0.015 Wb across an air gap of 2.5 mm long, having an effective area of 200 cm2. Solution : Φ 0.015 B 0.75 T 4 A 200 10 B 0.75 H 597000 A/m -7 0 4π 10 F Hl 597000 2.5 103 1492 At Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 14 Composite Magnetic Circuit Case 1 : l1 R1 1 A1 l2 R2 2 A2 l1 l2 T otalReluctance, R R 1 R 2 1 A1 2 A2 Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 15 mmf of coil T ot alflux, t ot alreluct ance F NI l1 l2 R 1 A1 2 A2 Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 16 Case 2 : (with air gap) Total reluctance, l1 l2 R 1 A 0 A 1 l1 l2 0 A ( 1 / 0 ) 1 l1 l2 0 A r Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 17 Since the relative permeability μr (= μ1/ μ0) of steel is very large (of the order of thousand), the major contribution in the total reluctance R is by the air-gap, though its length l2 may be quite small (say, a few millimetres). Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 18 Kirchhoff’s Laws Kirchhoff’s Flux Law (KFL) : The total magnetic flux towards a junction is equal to the total magnetic flux away from that junction. Kirchhoff’s Magnetomotive Force Law (KML) : In a closed magnetic circuit, the algebraic sum of the product of the magnetic field strength and the length of each part of the circuit is equal to the resultant magnetomotive force. Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 19 Steps to solve a problem on magnetic circuit Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 20 Review Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance (R). Analogy between Electric and Magnetic Circuits. Composite Magnetic Circuit. Monday, April 13, 2015 Ch. 6 Magnetic Circuits Next 21