Unit-4 Magnetic Circuits

1. Next Unit-4Magnetic Circuits

2. Next Topics to be Discussed • Magnetomotive Force (MMF). • Magnetic Field Strength (H). • Magnetic Permeability. • Reluctance (R). • Analogy between Electric and Magnetic Circuits. • Composite Magnetic Circuit. • Magnetic Leakage and Fringing. • Air Gaps in Magnetic Circuits. Ch. 6 Magnetic Circuits

3. Next 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. Ch. 6 Magnetic Circuits

4. Next 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. Ch. 6 Magnetic Circuits

5. Next 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 . Ch. 6 Magnetic Circuits

6. Next Magnetic Permeability (μ) • If the core of the toroid is vacuum or air, the magnetic flux densityB in the core bears a definite ratio to the magnetic field strengthH. • This ratio is called permeability of free space. • Thus, for vacuum or air, Ch. 6 Magnetic Circuits

7. Next • 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 permeabilityof the material. • Normally, we write μ = μr μ0. • μr is called relativepermeability (just a number). Ch. 6 Magnetic Circuits

8. Next 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). Ch. 6 Magnetic Circuits

9. Click Next Magnetic Circuit Theory • For a toroid, mmf,F = NIampere-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 Ch. 6 Magnetic Circuits

10. Comparing this with Next We get Ch. 6 Magnetic Circuits

11. Next Analogy between Electric and Magnetic Circuits Ch. 6 Magnetic Circuits

12. Next 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 : Ch. 6 Magnetic Circuits

13. Next Composite Magnetic Circuit Case 1 : Ch. 6 Magnetic Circuits

14. Next Ch. 6 Magnetic Circuits

15. Next Case 2 : (with air gap) Total reluctance, Ch. 6 Magnetic Circuits

16. Next • 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). Ch. 6 Magnetic Circuits

17. Next Magnetic Leakage and Fringing Ch. 6 Magnetic Circuits

18. Next • The flux lines, such as a, b and c, leak through the core. • This is called leakage flux, since it does not contribute to the useful flux passing through the metallic ring. • We define leakage factor as the ratio of total flux through the exciting winding to the useful flux. • The value of the leakage factor for electrical machines is about 1.15 to 1.25. Ch. 6 Magnetic Circuits

19. Next • There is another effect called fringing. • The useful flux passing across the air-gap tends to bulge outward. • This happens because the magnetic flux lines tend to repel each other in • Its effect is to cause a slight increase (say, about 10 %) in the cross-sectional area at the air gap. Ch. 6 Magnetic Circuits

20. Next 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. Ch. 6 Magnetic Circuits

21. Next Steps to solve a problem on magnetic circuit Ch. 6 Magnetic Circuits

22. Next Air Gaps in Magnetic Circuits • Two purposes : • To permit part of a magnetic circuit to move, for example, in relays and in electrical machines. • To make the magnetization characteristic of the circuit more linear. Ch. 6 Magnetic Circuits

23. Next Review • Magnetomotive Force (MMF). • Magnetic Field Strength (H). • Magnetic Permeability. • Reluctance (R). • Analogy between Electric and Magnetic Circuits. • Composite Magnetic Circuit. • Magnetic Leakage and Fringing. • Air Gaps in Magnetic Circuits. Ch. 6 Magnetic Circuits