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Chapter 6 Magnetic Circuits  D D.C. Kulshreshtha Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 3 Thought of the DAY There are no secrets to success. It is the result of preparation, hard work, and learning from failure. --Colin Powell.. Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 4 Topics to be Discussed Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance ( R ). Analogy between Electric and Magnetic Circuits. Composite Magnetic Circuit. Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 5 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. Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 6 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. Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 7 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. Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 8 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, Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 9 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 = μ r μ 0. μ r is called relative permeability (just a number). Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 10 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, The reciprocal of reluctance is known as permeance ( G ). Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 11 Magnetic Circuit Theory For a toroid, mmf, F = N I a mpere-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 = B  A Dividing, we get Next Click

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 12 Comparing this with We get Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 13 Analogy between Electric and Magnetic Circuits Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 14 Example 1 Calculate the magnetomotive force (mmf) required to produce a flux of Wb across an air gap of 2.5 mm long, having an effective area of 200 cm 2. Solution : Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 15 Composite Magnetic Circuit Case 1 : Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 16 Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 17 Case 2 : (with air gap) Total reluctance, Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 18 Since the relative permeability μ r (= μ 1 / μ 0 ) 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 l 2 may be quite small (say, a few millimetres). Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 19 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. Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 20 Steps to solve a problem on magnetic circuit Next

Friday, February 26, 2016 Ch. 6 Magnetic Circuits 21 Review Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance ( R ). Analogy between Electric and Magnetic Circuits. Composite Magnetic Circuit. Next