ELE 1001: Basic Electrical Technology
L-8
MAGNETIC CIRCUITS
Dept. of E & E, MIT, Manipal
1
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
2
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
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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
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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
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ELE 1001: Basic Electrical Technology
Series Magnetic Circuit
S  S1  S 2  S3  S g
Total Re luc tance
Where S1 
l1
μ0 μr1a1
S2 
l2
μ0 μr 2 a2
S3 
l3
μ0 μr 3a3
Sg 
lg
μ0 μrg a g
Ring shaped series magnetic circuit with air-gap
 B1l1
Bg l g
B
l
B
l
3
3
2
2
m m f : φ1S1  φ2 S 2  φ3 S3  φg S g   



μ μ
 0 r1 μ0 μr 2 μ0 μr 3 μ0 μrg
Total m mf : H1l1  H 2l2  H 3l3  H g l g
Dept. of E & E, MIT, Manipal
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



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
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ELE 1001: Basic Electrical Technology
Fringing Effect
 Effectively it increases the cross sectional area of air
gap.
Dept. of E & E, MIT, Manipal
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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
Leakage Coefficient λ 
T otalflux of coil
Usefulflux
Dept. of E & E, MIT, Manipal
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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).
Dept. of E & E, MIT, Manipal
Hysteresis loop
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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.
Dept. of E & E, MIT, Manipal
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ELE 1001: Basic Electrical Technology
Losses in Magnetic Circuit
Eddy current loss
• 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
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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.
(i)
(ii)
(iii)
(iv)
(v)
Dept. of E & E, MIT, Manipal
1400 AT
0.762 Wb/m^2
0.538mWb
2.6×10^6 AT/Wb
972
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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
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