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BASIC ELECTRICAL ENGINEERING
D. C. KULSHRESHTHA,
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Chapter 6
Magnetic Circuits

D.C. Kulshreshtha
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Thought of the DAY
There are no secrets to success.
It is the result of
preparation, hard work,
and learning from
failure.
--Colin Powell..
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Ch. 6 Magnetic Circuits
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Topics to be Discussed



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
Magnetomotive Force (MMF).
Magnetic Field Strength (H).
Magnetic Permeability.
Reluctance (R).
Analogy between Electric and Magnetic
Circuits.
Composite Magnetic Circuit.
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Ch. 6 Magnetic Circuits
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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.
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Magnetomotive Force (MMF)




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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.
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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 .
F IN
H 
l
l
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Magnetic Permeability (μ)

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If the core of the toroid is vacuum or air, the
magnetic flux density B in the core bears a
definite ratio to the magnetic field strength H.
This ratio is called permeability of free space.
Thus, for vacuum or air,
B
7
 0  4 10 Tm/A
H
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
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 permeability of the material.

Normally, we write μ = μr μ0.

μr is called relative permeability (just a number).
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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,
1 l
1 l
R 

 A  r 0 A
The reciprocal of reluctance is known as
permeance (G).
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Magnetic Circuit Theory

For a toroid, mmf, F = NI ampere-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
Click
F
Φ BA B A
A
A


    r 0
 Φ
l /( r 0 A)
F Hl H l
l
l

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E
I
R
Comparing this with
1
l
We get R 
r 0 A
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Analogy between Electric and Magnetic Circuits
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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 :

Φ
0.015
B 
 0.75 T
4
A 200 10
B
0.75
H

 597 000 A/m
-7
 0 4π 10
F  Hl  597 000  2.5 103  1492 At
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Composite Magnetic Circuit
Case 1 :
l1
R1 
1 A1
l2
R2 
 2 A2
l1
l2
 Total Reluctance , R  R 1  R 2 

1 A1  2 A2
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mmf of coil
 Total flux,  
total reluctance
F
NI
 
l1
l2
R

1 A1  2 A2
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Case 2 : (with air gap)
Total reluctance,
l1
l2
R 

1 A  0 A

1  l1


 l2 
0 A  (1 / 0 )


1  l1
  l2 

0 A   r

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
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).
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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.
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Steps to solve a problem on magnetic circuit
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Review

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Magnetomotive Force (MMF).
Magnetic Field Strength (H).
Magnetic Permeability.
Reluctance (R).
Analogy between Electric and Magnetic
Circuits.
Composite Magnetic Circuit.
Saturday, April 29, 2017
Ch. 6 Magnetic Circuits
Next
21