USE OF ICT IN EDUCATION FOR ONLINE AND BLENDED LEARNING-IIT BOMBAY BIRLA INSTITUTE OF TECHNOLOGY MESRA, RANCHI ASSIGNMENT( MODULE MAGNETIC CIRCUIT) Submitted by: Dr. Deepak Kumar(Group Leader) Dr. Vikash Kumar Gupta

Magnetic Fields In the region surrounding a permanent magnet there exists a magnetic field, which can be represented by magnetic flux lines similar to electric flux lines. Magnetic flux lines differ from electric flux lines in that they don’t have an origin or termination point. Magnetic flux lines radiate from the north pole to the south pole through the magnetic bar. 3

Magnetic Fields Continuous magnetic flux lines will strive to occupy as small an area as possible. The strength of a magnetic field in a given region is directly related to the density of flux lines in that region. If unlike poles of two permanent magnets are brought together the magnets will attract, and the flux distribution will be as shown below. 4

Magnetic Fields If like poles are brought together, the magnets will repel, and the flux distribution will be as shown. If a nonmagnetic material, such as glass or copper, is placed in the flux paths surrounding a permanent magnet, there will be an almost unnoticeable change in the flux distribution. 5

Magnetic Fields If a magnetic material, such as soft iron, is placed in the flux path, the flux lines will pass through the soft iron rather than the surrounding air because the flux lines pass with greater ease through magnetic materials than through air. This principle is put to use in the shielding of sensitive electrical elements and instruments that can be affected by stray magnetic fields. 6

Magnetic Fields The direction of the magnetic flux lines can be found by placing the thumb of the right hand in the direction of conventional current flow and noting the direction of the fingers (commonly called the right hand rule). 7

Magnetic Fields Flux and Flux Density In the SI system of units, magnetic flux is measured in webers (Wb) and is represented using the symbol . The number of flux lines per unit area is called flux density (B). Flux density is measured in teslas (T). Its magnitude is determined by the following equation: 8

Magnetic Fields Permeability If cores of different materials with the same physical dimensions are used in the electromagnet, the strength of the magnet will vary in accordance with the core used. The variation in strength is due to the number of flux lines passing through the core. Magnetic material is material in which flux lines can readily be created and is said to have high permeability. Permeability () is a measure of the ease with which magnetic flux lines can be established in the material. 9

Magnetic Fields Permeability Permeability of free space 0 (vacuum) is Materials that have permeability slightly less than that of free space are said to be diamagnetic and those with permeability slightly greater than that of free space are said to be paramagnetic. 10

Magnetic Fields Permeability Magnetic materials, such as iron, nickel, steel and alloys of these materials, have permeability hundreds and even thousands of times that of free space and are referred to as ferromagnetic. The ratio of the permeability of a material to that of free space is called relative permeability. 11

Inductance Inductors are designed to set up a strong magnetic field linking the unit, whereas capacitors are designed to set up a strong electric field between the plates. Inductance is measure in Henries (H). One henry is the inductance level that will establish a voltage of 1 volt across the coil due to a chance in current of 1 A/s through the coil.

Inductor construction and inductance

Magnetic Materials Iron, Cobalt and Nickel and various other alloys and compounds made using these three basic elements magckt

A Few Definitions Related to Electromagnetic Field  (Unit is Weber (Wb)) = Magnetic Flux Crossing a Surface of Area ‘A’ in m2. B (Unit is Tesla (T)) = Magnetic Flux Density = /A H (Unit is Amp/m) = Magnetic Field Intensity =  = permeability = o r o = 4*10-7 H/m = Permeability of free space (air) r = Relative Permeability r >> 1 for Magnetic Material magckt

Ampére’s Law The line integral of the magnetic field intensity around a closed path is equal to the sum of the currents flowing through the area enclosed by the path. magckt

Example of Ampére’s Law Find the magnetic field along a circular path around an infinitely long Conductor carrying ‘I’ ampere of current. 900 B,H r dl are perpendicular to radius ‘r’ at any point ‘A’ Since both and on the circular path, the angle  is zero between them at all points. Also since all the points on the circular path are equidistant from the current carrying conductor is constant at all points on the circle or magckt

Magnetic Circuits They are basically ferromagnetic structures(mostly Iron, Cobalt, Nickel alloys and compounds) with coils wound around them. Because of high permeability most of the magnetic flux is confined within the magnetic circuit. Thus is always aligned with Examples: Transformers,Actuators, Electromagnets, Electric Machines magckt

Magnetic Circuits w I N d l= mean length magckt

Magnetic Circuits F =NI= Magneto Motive Force or MMF = # of turns * Current passing through it F = NI = Hl (why!) or or or or = Reluctance of magnetic path magckt

Analogy Between Magnetic and Electric Circuits F =MMF is analogous to Electromotive force (EMF) =E = Flux is analogous to I = Current = Reluctance is analogous to R = Resistance = Permeance ; Analogous to conductance magckt

Magnetization Curves saturation B knee B Linear H H (linear) (Ideal) Magnetization curve (non-linear) (Actual) (see also Fig. 1.6 in the text) magckt

Magnetization Curves One can linearize magnetic circuits by including air-gaps However that would cause a large increase in ampere-turn requirements. Ex: Transformers don’t have air-gaps. They have very little magnetizing current (5% of full load) Induction motors have air-gaps. They have large magnetizing current (30-50%) Question: why induction motors have air –gap and transformers don’t? magckt

Magnetization Circuits with Air-gap lc w i lg N d magckt

Fringing lc w i N With large air-gaps, flux tends to leak outside the air –gap. This is called fringing which increases the effective flux area. One way to approximate this increase is: magckt

Magnetization Curves (for examples) magckt

Inductance(L) Definition: Flux Linkage() per unit of current(I) in a magnetic circuit I N Thus inductance depends on the geometry of construction magckt

Faraday’s law of Electromagnetic Induction The EMF (Electromotive Force) induced in a magnetic circuit is Equal to the rate of change of flux linked with the circuit magckt

Lenz’s Law The polarity of the induced voltage is given by Lenz’s law The polarity of the induced voltage will be such as to oppose the very cause to which it is due Thus sometimes we write magckt

What will non-linearity in magnetic circuit lead to? It would cause distortion in current waveforms since by Faraday’s and Lenz’s law the induced voltage always has to balance out the applied voltage that happens to be sinusoidal magckt

Energy Stored by an Inductor The ideal inductor, like the ideal capacitor, does not dissipate the electrical energy supplied to it. It stores the energy in the form of a magnetic field. Joules,J 26

Iron Losses in Magnetic Circuit There are two types of iron losses Hysteresis losses Eddy Current Losses Total iron loss is the sum of these two losses magckt

Hysteresis losses i f =frequency of sine source B i Br t H Hc B-H or Hysteresis loop Br saturation 3 knee point 4 5 1 2 1 2 3 t H Hc 4 5 Br = Retentive flux density (due to property of retentivity) Hc= Coercive field intensity (due to property of coercivity) magckt

Hysteresis losses = khBnmaxf The lagging phenomenon of B behind H is called hysteresis The tip of hysteresis loops can be joined to obtain the magnetization characteristics In each of the current cycle the energy lost in the core is proportional to the area of the B-H loop Energy lost/cycle = Vcore Ph = Hysteresis loss = f Vcore = khBnmaxf kh = Constant, n = 1.5-2.5, Bmax= Peak flux density magckt

Eddy current loss Laminations flux flux Current = keB2maxf , Because of time variation of flux flowing through the magnetic material as shown, current is induced in the magnetic material, following Faraday’s law. This current is called eddy current. The direction of the current is determined by Lenz’s law. This current can be reduced by using laminated (thin sheet) iron structure, with Insulation between the laminations. Pe = Eddy current loss = keB2maxf , ke = Constant Bmax= Peak flux density magckt

Magnetically Coupled Circuits FARADAY’S LAW The physical or experimental law governing the principle of magnetic induction . “The electromotive force (EMF) induced in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit.” The EMF can either be produced by changing B (induced EMF) or by changing the area, e.g., by moving the wire (motional EMF).

Self Inductance According to Faraday’s law, the voltage induced in a coil is proportional to the number of turns N and the time rate of change of the magnetic flux φ.

Self Inductance L is the inductance of the inductor commonly called self-inductance (relating the induced voltage in a coil by a time-varying current in the same coil)

Mutual Inductance Two coils in a close proximity are linked together by the magnetic flux produced by current in one coil, thereby inducing voltage in the other. the two coils are said to be magnetically coupled although they are physically apart. MUTUAL INDUCTANCE is the ability of one inductor to induce a voltage across a neighbouring inductor, measured in henrys (H). Mutual coupling only exists when the coils are in close proximity, and the circuits are driven by time-varying sources.

Mutual Inductance M21 is mutual inductance of coil 2 w.r.t coil 1

Mutual Inductance M12 is mutual inductance of coil 1 w.r.t. coil 2

Dot Convention M21=M12=M , and is always a positive quantity . The induced voltage may be positive or negative. The choice of polarity is made by examining the way in which both coils are physically wound and applying Lenz’ Law in conjunction with Right-Hand rule. The procedure is inconvenient in circuit analysis since it is difficult to show the construction details of the coil in circuit schematics. Hence use the dot convention. If a current enters (leaves) the dotted terminals of one coil, the reference polarity of the mutual voltage in the second coil is positive (negative) at the dotted terminal of the second coil. magckt

DOT CONVENTION

DOT CONVENTION

DOT CONVENTION

Dot Convention Series-aiding Connection: L=L1+L2+2M Series-opposition Connection: L=L1+L2-2M magckt

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