1. L-8 MAGNETIC CIRCUITS ELE 1001: Basic Electrical Technology
Dept. of E & E, MIT, Manipal

2. ELE 1001: Basic Electrical Technology
Objectives
To solve various kinds of problems involving series magnetic circuits.
To understand losses involved in magnetic circuits.
Dept. of E & E, MIT, Manipal

3. Contents Series magnetic circuit Fringing effect
ELE 1001: Basic Electrical Technology
Contents
Series magnetic circuit
Fringing effect
Useful flux and leakage flux
Magnetic hysteresis
Losses in magnetic circuit
Dept. of E & E, MIT, Manipal

4. Series Magnetic Circuit
ELE 1001: Basic Electrical Technology
Series Magnetic Circuit
Flux ɸ is the same in all sections if leakage flux is neglected.
Flux density and reluctance in each section may vary, depending on its effective cross-sectional area and material.
Rectangular shaped series magnetic circuit with air gap.
Dept. of E & E, MIT, Manipal

5. Series Magnetic Circuit
ELE 1001: Basic Electrical Technology
Series Magnetic Circuit
Equivalent reluctance is the sum of reluctance of different parts/elements.
The resultant MMF is the sum of MMFs in each individual parts/elements
Dept. of E & E, MIT, Manipal

6. Series Magnetic Circuit
ELE 1001: Basic Electrical Technology
Series Magnetic Circuit
Ring shaped series magnetic circuit with air-gap
Dept. of E & E, MIT, Manipal

7. ELE 1001: Basic Electrical Technology
Fringing Effect
Air gap is practically an unavoidable part of any magnetic circuit, in which there is a relative movement between different parts.
(e.g. in motors, generators, relays, etc.)
Due to increased reluctance of the air gap the flux spreads into the surrounding medium causing flux fringing effect.
Dept. of E & E, MIT, Manipal

8. ELE 1001: Basic Electrical Technology
Fringing Effect
Effectively it increases the cross sectional area of air gap.
Dept. of E & E, MIT, Manipal

9. Useful Flux and Leakage Flux
ELE 1001: Basic Electrical Technology
Useful Flux and Leakage Flux
Magnetic leakage : The passage of magnetic flux outside the path along which it can do useful work.
Total flux of coil = Useful flux + Leakage flux
Dept. of E & E, MIT, Manipal

10. ELE 1001: Basic Electrical Technology
Magnetic Hysteresis:
Lagging of magnetization or flux density behind the magnetizing force.
Residual magnetism : Magnetic flux remains in the ferromagnetic material even though the magnetizing force is made zero (Br)
Coercive force : The magnetizing force required to remove the residual magnetism from the material (Hc).
Hysteresis loop
Dept. of E & E, MIT, Manipal

11. Losses in Magnetic Circuit
ELE 1001: Basic Electrical Technology
Losses in Magnetic Circuit
Hysteresis loss
The energy dissipated as heat in the process of magnetization and demagnetization which is proportional to the area of hysteresis loop.
‘Soft' magnetic materials with low hysteresis loss , such as silicon steel, are usually used in cores of electric machines like motors, generators and transformers.
Steinmetz empirical formula for hysteresis loss:
Hysteresis loss per unit volume=Ph=〖"Kh*f*Bmax" 〗^𝑛
"Kh" depends on the material,
N=Steinmetz exponent,may vary from 1.5 to 2.5. For iron it may be taken as 1.6.
Eddy current loss per unit volume
kef2Bmax2τ2
K is constant and τ is thickness of plate
Dept. of E & E, MIT, Manipal

12. Losses in Magnetic Circuit
ELE 1001: Basic Electrical Technology
Eddy current loss
Losses in Magnetic Circuit
The varying flux in the magnetic core induces emf and hence eddy current within the material.
Flow in closed loops in planes perpendicular to the magnetic field
Results in loss of power and heating of the material.
Cores of electric machines are laminated to reduce eddy current loss
Dept. of E & E, MIT, Manipal

13. ELE 1001: Basic Electrical Technology
Exercise 1
A steel ring 25cm mean diameter and of circular section 3cm in diameter has an air-gap of 1.5mm length. It is wound uniformly with 700 turns of wire carrying a current of 2A. Calculate (i) magneto motive force (ii) flux density (iii) magnetic flux (iv) reluctance and (v) relative permeability of steel ring.
Neglect magnetic leakage and assume that iron path takes about 35% of the total magneto motive force.
1400 AT
0.762 Wb/m^2
0.538mWb
2.6×10^6 AT/Wb
972
Dept. of E & E, MIT, Manipal

14. ELE 1001: Basic Electrical Technology
Summary
Only one flux path is available in series magnetic circuit and equivalent reluctance is the sum of reluctance of different parts.
Losses occurring in magnetic circuits are classified as hysteresis and eddy current losses.
Dept. of E & E, MIT, Manipal