PROPRIETARY MATERIAL. 2010 The McGraw-Hill Companies, Inc. All rights reserved. No part of this PowerPoint slide may be displayed, reproduced or distributed

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BASIC ELECTRICAL ENGINEERING

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D. C. KULSHRESHTHA,

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Chapter 6Magnetic Circuits

D.C. Kulshreshtha

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Saturday, May 6, 2023 Ch. 6 Magnetic Circuits 3

Thought of the DAYThere are no secrets to success.

It is the result of preparation, hard work,

and learning fromfailure.

--Colin Powell..

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Topics to be DiscussedTopics to be Discussed Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance (R). Analogy between Electric and Magnetic

Circuits. Composite Magnetic Circuit.

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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) 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 .

lIN

lH

F

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Magnetic Permeability (μ) 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,

Tm/A104 70

HB

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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,

Al

Al

r 0

11

R

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

lA

lA

lA

HB

HlBAΦ

r 0F )/( 0 Al

ΦrF

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Comparing this with REI

We getAl

r 0

1

R

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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 :

T0.7510200

015.04

A

ΦB

A/m00059710π475.0

7-0

BH

At1492 3105.2000597HlF

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Composite Magnetic Circuit

11

11 A

l

R

22

22 A

l

R

22

2

11

121,Reluctance Total

Al

Al

RRR

Case 1 :

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22

2

11

1

reluctance totalcoil of mmf flux, Total

Al

Al

NI

RF

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Case 2 : (with air gap)

Total reluctance,

Al

Al

0

2

1

1

R

2

01

1

0 )/(1 llA

2

1

0

1 llA 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 Review Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance (R). Analogy between Electric and Magnetic

Circuits. Composite Magnetic Circuit.

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PROPRIETARY MATERIAL. 2010 The McGraw-Hill Companies, Inc. All rights reserved. No part of this PowerPoint slide may be displayed, reproduced or distributed