1. Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1

2. Magnetic Fields – Ch 11 Introduction to Inductors Faraday’s Law of Electromagnetic Induction Lenz’s Law (& Magnetic Field, Permeability – Ch 11) Permeability (μ) – Ch 11 Self Induction Types of Inductors 06/08/2015 2

3. In the region surrounding a permanent magnet there exists a magnetic field, which can be represented by magnetic flux lines Flux in dictionary – fluctuation, change, unrest Magnetic flux lines, do not have origins or terminating points and exist in continuous loops and radiate from north to south pole returning to the north pole through the metallic bar Symbol for magnetic flux is the Greek letter Φ (phi).

4. Magnetic flux line will occupy as small an area as possible, which results in magnetic flux lines of minimum length between the poles. The strength of a magnetic field in a particular region is directly related to the density of flux lines. In fig, the magnetic field strength at a is twice than at b since twice as many magnetic flux lines are associated with the perpendicular plane at a than at b.

5. If unlike poles of two permanent magnets are brought together, the magnets will attract, and the flux distribution will be as shown in Fig 11.2. If like poles are brought together, the magnets will repel, and the flux distribution will be as shown in Fig. 11.3.

6. 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 (Fig. 11.4).

7. If a magnetic material, such as soft iron, is placed in the flux path, the flux lines will pass through the soft iron with greater ease through magnetic materials than through air. Above principle is used in the shielding of sensitive electrical elements / instruments that can be affected by stray magnetic fields.

8. we shall consider a third element, the inductor, which has a number of response characteristics similar in many respects to those of the capacitor. Inductors are coils of various dimensions designed to introduce specified amounts of inductance into a circuit. 06/08/2015 8

9. If a conductor is moved through a magnetic field so that it cuts magnetic lines of flux, a voltage will be induced across conductor. The greater the number of flux lines cut per unit time (by increasing speed), or stronger the magnetic field strength (for same traversing speed), the greater will be the induced voltage across the conductor. 06/08/2015 9 or if the conductor is held fixed and the magnetic field is moved so that its flux lines cut the conductor, the same effect will be produced.

10. If a coil of N turns is placed in the region of a changing flux, as in fig, a voltage will be induced across the coil as: Faraday’s law: 06/08/2015 10 where N represents the number of turns of the coil and dΦ/dt is the instantaneous change in flux (in webers) linking the coil.

11. The term linking refers to the flux within the turns of wire. The term changing simply indicates if the flux linking the coil ceases to change, such as when the coil simply sits still in a magnetic field of fixed strength, dΦ/dt = 0, and the induced voltage e = N(dΦ/dt) = N(0) = 0.. Faraday’s law: 06/08/2015 11

12. Lenz’s law, states that an induced effect is always such as to oppose the cause that produced it. But to understand it we need to study magnetic field and its relationship with current. 06/08/2015 12

13. A magnetic field (represented by concentric flux lines) is present around every wire carrying electric current. The direction of the magnetic flux lines can be found simply by placing the thumb of the right hand in the direction of conventional current flow and noting the direction of the fingers. (Called as right-hand rule.)

14. If the conductor is wound in a single-turn coil, the resulting flux will flow in a common direction through the centre of the coil. A coil of more than one turn would produce a magnetic field in a continuous path through and around the coil (Fig. 11.8). The flux lines leaving the coil from the left and entering to the right simulate a north and a south pole, respectively.

15. Flux distribution or field strength of coil is quite similar to but weaker than a permanent magnet. However, it can be effectively increased by placing a core of certain materials, (iron, steel, or cobalt, etc) within the coil to increase the flux density within coil. With the addition of a core, we have devised an electromagnet whose field strength can be varied by changing one of the component values (current, turns, and so on).

16. For same physical dimensions, strength of the electromagnet will vary in accordance with the material of core used. This variation in strength is due to the greater or lesser number of flux lines passing through the core. Materials in which flux lines can readily be set up are said to be magnetic and to have high permeability.

17. The permeability (μ) of a material, therefore, is a measure of the ease with which magnetic flux lines can be established in the material. It is similar to conductivity in electric circuits. The permeability of free space μ o (vacuum) is Practically speaking, the permeability of all non- magnetic materials, such as copper, aluminium, wood, glass, and air, is the same as that for free space.

18. Materials that have permeability slightly less than that of free space are said to be diamagnetic, Those with permeability slightly greater than that of free space are said to be paramagnetic. Magnetic materials, such as iron, nickel, steel, cobalt, and alloys of these metals, have permeability hundreds and even thousands of times that of free space. Materials with these very high permeability are referred to as ferromagnetic.

19. The ratio of the permeability of a material to that of free space is called its relative permeability μ r ; that is, In general, for ferromagnetic materials, μ r ≥ 100, and for nonmagnetic materials, μ r = 1.

20. The direction of flux lines can be determined for the electromagnet by placing the fingers of the right hand in the direction of current flow around the core. The thumb will then point in the direction of the north pole of the induced magnetic flux.

21. We now know from magnetic circuits that if the current increases in magnitude, the flux linking the coil also increases. However, only a changing flux linking a coil induces a voltage across the coil. 06/08/2015 21

22. For this coil, therefore, an induced voltage is developed across the coil due to the change in current through the coil. The polarity of this induced voltage (e ind ) tends to establish a current in the coil that produces a flux that will oppose any change in the original flux. 06/08/2015 22

23. The instant the current begins to increase in magnitude, there will be an opposing effect trying to limit the change. It is “choking” the change in current through the coil. Hence, the term choke is often applied to the inductor or coil. Thus Lenz’s law, states that an induced effect is always such as to oppose the cause that produced it. 06/08/2015 23

24. This ability of a coil (Lenz’s Law) to oppose any change in current is a measure of the self-inductance L of the coil. For brevity, prefix self is usually dropped. Inductance is measured in henries (H), after the American physicist Joseph Henry. Inductors are coils of various dimensions designed to introduce specified amounts of inductance into a circuit. 06/08/2015 24

25. The inductance of a coil varies directly with the magnetic properties of the coil. Ferromagnetic materials, therefore, are frequently employed to increase the inductance by increasing flux linking the coil. A close approximation can be found by 06/08/2015 25

26. where N represents the number of turns; μ, the permeability of the core (note that μ is not a constant and depends on other magnetizing parameters); A, the area of the core in square meters; and ℓ is the mean length of core in meters. Substituting μ = μ r μ o ;.And thus 06/08/2015 26 where L o is the inductance of the coil with an air core.

27. Equations for the inductance of coils different from those shown above can be found in reference handbooks. Most of the equations are more complex than just described. 06/08/2015 27 Figures show inductor configurations for which above equation is appropriate.

28. Example – Find the inductance of the air-core coil and with iron core μ r = 2000. Solution: And with iron core 06/08/2015 28

29. Practical Equivalence Inductors, like capacitors, are not ideal. Every inductor has a resistance equal to resistance of turns and a stray capacitance due to the capacitance between the turns of the coil. However, stray capacitance can be ignored, resulting in the equivalent model 06/08/2015 29

30. Practical Equivalence For most applications, we have been able to treat the capacitor as an ideal element and maintain a high degree of accuracy. For the inductor, however, R L must often be included in the analysis and can have a pronounced effect on the response of a system (Chapter 20, “Resonance”). 06/08/2015 30

31. Practical Equivalence The level of R L can extend from a few ohms to a few hundred ohms. Note that the longer or thinner the wire used in the construction of the inductor, the greater will be the dc resistance as determined by R = ρl /A. However, in our initial analysis we will treat the inductor as an ideal element. 06/08/2015 31

32. Symbols Appearance Fixed Inductor: The fixed air-core and iron-core inductors already discussed. Variable Inductor: The permeability-tuned variable coil has a ferromagnetic shaft that can be moved within the coil to vary the flux linkages of the coil and thereby its inductance. 06/08/2015 32

33. Testing The primary reasons for inductor failure are shorts that develop between the windings and open circuits in the windings due to factors such as excessive currents, overheating, and age. The open-circuit condition can be checked easily with an ohmmeter (∞ ohms indication), but the short-circuit condition is harder to check because the resistance of many good inductors is relatively small. A short between the windings and the core can be checked by simply placing one lead of the meter on one wire (terminal) and the other on the core itself. An indication of zero ohms reflects a short between the two because the wire that makes up the winding has an insulation jacket throughout. 06/08/2015 33 LCR meter

34. Standard Values and Recognition Factor Like the capacitor, the most common employ the same numerical multipliers / tolerances as the most common resistors. In general, therefore, we find inductors with the following multipliers: 0.1 μH, 0.12 μ H, 0.15 μ H, 0.18 μ H, 0.22 μ H, 0.27 μ H, 0.33 μ H, 0.39 μ H, 0.47 μ H, 0.56 μ H, 0.68 μH, and 0.82 μ H, and then 1 mH, 1.2 mH, 1.5 mH, 1.8 mH, 2.2 mH, 2.7 mH, and so on. 06/08/2015 34

35. Standard Values and Recognition Factor 06/08/2015 35

36. Standard Values and Recognition Factor 06/08/2015 36

37. Standard Values and Recognition Factor 06/08/2015 37

38. Standard Values and Recognition Factor 06/08/2015 38

39. Standard Values and Recognition Factor 06/08/2015 39

40. Magnetic Fields – Ch 11 Introduction to Inductors Faraday’s Law of Electromagnetic Induction Lenz’s Law (& Magnetic Field, Permeability – Ch 11) Permeability (μ) – Ch 11 Self Induction Types of Inductors 06/08/2015 40

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