BASIC ELECTRICAL ENGINEERING

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Topics to be DiscussedTopics to be DiscussedMagnetomotive Force (MMF).Magnetomotive Force (MMF).Magnetic Field Strength (Magnetic Field Strength (HH).).Magnetic Permeability.Magnetic Permeability.Reluctance (Reluctance (RR).).Analogy between Electric and Magnetic Analogy between Electric and Magnetic Circuits.Circuits.Composite Magnetic Circuit.Composite Magnetic Circuit.Magnetic Leakage and Fringing.Magnetic Leakage and Fringing.Air Gaps in Magnetic Circuits.Air Gaps in Magnetic Circuits.

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IntroductionIntroductionUnlike electric field lines, the lines of Unlike electric field lines, the lines of magnetic magnetic fluxflux form form closed loopsclosed loops..

A A magnetic circuitmagnetic circuit is a closed path followed by is a closed path followed by lines of magnetic flux.lines of magnetic flux.

A copper wire, because of its high A copper wire, because of its high conductivity,conductivity,confines the electric current within itself.confines the electric current within itself.

Similarly, a ferromagnetic material (such as iron Similarly, a ferromagnetic material (such as iron or steel), due to its high or steel), due to its high permeabilitypermeability, confines , confines magnetic flux within itself. magnetic flux within itself.

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Magnetomotive Force (MMF)Magnetomotive Force (MMF)The electric current is due to the existence of an The electric current is due to the existence of an electromotive force (emf). electromotive force (emf). By analogy, we may say that in a magnetic circuit, the By analogy, we may say that in a magnetic circuit, the magnetic flux is due to the existence of a magnetic flux is due to the existence of a magnetomotive magnetomotive forceforce ((mmfmmf).).mmf is caused by a current flowing through one or more mmf is caused by a current flowing through one or more turns. turns. The value of the mmf is proportional to the current and The value of the mmf is proportional to the current and the number of turns. the number of turns. It is expressed in It is expressed in ampere turnsampere turns ((AtAt). ). But for the purpose of dimensional analysis, it is But for the purpose of dimensional analysis, it is expressed in expressed in amperes.amperes.

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Magnetic Field Strength (Magnetic Field Strength (HH))The mmf per metre length of the magnetic circuitThe mmf per metre length of the magnetic circuit is is termed as the termed as the magnetic field strengthmagnetic field strength, , magnetic magnetic field intensityfield intensity, or , or magnetizing forcemagnetizing force..It units are It units are ampereampere--turns per metreturns per metre ((At/mAt/m) .) .Its value is independent of the medium .Its value is independent of the medium .

lIN

lH ==

F

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Magnetic Permeability (Magnetic Permeability (μμ))If the core of the toroid is If the core of the toroid is vacuumvacuum or or air,air, the the magnetic flux densitymagnetic flux density BB in the core bears a in the core bears a definite ratio to the definite ratio to the magnetic field strengthmagnetic field strength H.H.This ratio is called This ratio is called permeability of free spacepermeability of free space..Thus, for vacuum or air,Thus, for vacuum or air,

Tm/A104 70

−×== πμHB

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The flux produced by the given mmf is greatly The flux produced by the given mmf is greatly increased, if iron replaces the air in the core.increased, if iron replaces the air in the core.

As a result, the flux density As a result, the flux density B B also increases many also increases many times. times.

In general, we can write In general, we can write B B = = μμHH..

μμ is called the is called the permeabilitypermeability of the material.of the material.

Normally, we write Normally, we write μμ = = μμr r μμ00..

μμr r is called is called relativerelative permeability permeability (just a number).(just a number).

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Reluctance (Reluctance (RR) and Permeance () and Permeance (GG))The current in an electric circuit is limited by the The current in an electric circuit is limited by the presence of presence of resistanceresistance of the electric circuit.of the electric circuit.Similarly, the flux Similarly, the flux ΦΦ in a magnetic circuit is in a magnetic circuit is limited by the presence of the limited by the presence of the reluctancereluctance of the of the magnetic circuit, magnetic circuit,

Al

Al

r 0

11μμμ

==R

The reciprocal of reluctance is known as permeance (G).

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Magnetic Circuit TheoryMagnetic Circuit TheoryFor a toroid, mmf,For a toroid, mmf, FF = = NINI ampereampere--turns.turns.Because of this mmf, a magnetic field of Because of this mmf, a magnetic field of strength strength HH is set up throughout the length is set up throughout the length ll..Therefore, Therefore, FF = = HlHlIf, If, BB is the flux density, total flux is given as is the flux density, total flux is given as

ΦΦ = = BB ×× AADividing, we getDividing, we get ⇒====

lA

lA

lA

HB

HlBAΦ

r 0μμμF )/( 0 Al

ΦrμμF

=

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Comparing this with Comparing this with REI =

We getAl

r 0

1μμ

=R

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Analogy between Electric and Magnetic Circuits

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Example 1Example 1Calculate the magnetomotive force (mmf) Calculate the magnetomotive force (mmf) required to produce a flux of 0.015 Wb required to produce a flux of 0.015 Wb across an air gap of 2.5 mm long, having an across an air gap of 2.5 mm long, having an effective area of 200 cmeffective area of 200 cm22..

Solution :Solution :T0.75

10200015.0

4 =×== −A

ΦB

A/m00059710π475.0

7-0

=×

==μBH

At1492=××== −3105.2000597HlF

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Composite Magnetic CircuitComposite Magnetic Circuit

11

11 A

lμ

=R

22

22 A

lμ

=R

22

2

11

121,Reluctance Total

Al

Al

μμ+=+=∴ RRR

Case 1 :

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22

2

11

1

reluctance totalcoil of mmf flux, Total

Al

Al

NI

μμ+

==

=Φ∴

RF

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Case 2 : (with air gap)

Total reluctance,

Al

Al

0

2

1

1

μμ+=R

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 2

01

1

0 )/(1 llA μμμ

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 2

1

0

1 llA rμμ

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Since the relative permeability Since the relative permeability μμrr (= (= μμ11// μμ00) of ) of steel is very large (of the order of thousand), steel is very large (of the order of thousand), the major contribution in the total reluctance the major contribution in the total reluctance R R is by the airis by the air--gap, though its length gap, though its length ll22 may be may be quite small (say, a few millimetres). quite small (say, a few millimetres).

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Magnetic Leakage and FringingMagnetic Leakage and Fringing

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The flux lines, such as a, b and c, The flux lines, such as a, b and c, leakleak through through the core. the core. This is called This is called leakage fluxleakage flux, since it does not , since it does not contribute to the contribute to the useful fluxuseful flux passing through passing through the metallic ring. the metallic ring. We define We define leakage factorleakage factor as the ratio of total as the ratio of total flux through the exciting winding to the useful flux through the exciting winding to the useful flux. flux. The value of the leakage factor for electrical The value of the leakage factor for electrical machines is about 1.15 to 1.25.machines is about 1.15 to 1.25.

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There is another effect called There is another effect called fringingfringing..

The useful flux passing across the airThe useful flux passing across the air--gap gap tends to bulge outward. tends to bulge outward.

This happens because the magnetic flux lines This happens because the magnetic flux lines tend to repel each other in tend to repel each other in

Its effect is to cause a slight increase (say, Its effect is to cause a slight increase (say, about 10 %) in the crossabout 10 %) in the cross--sectional area at the sectional area at the air gap. air gap.

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KirchhoffKirchhoff’’s Lawss LawsKirchhoffKirchhoff’’s Flux Laws Flux Law ((KFL)KFL) :: The total The total magnetic flux towards a junction is equal to the magnetic flux towards a junction is equal to the total magnetic flux away from that junction.total magnetic flux away from that junction.

KirchhoffKirchhoff’’s Magnetomotive Force Laws Magnetomotive Force Law ((KML)KML):: In a closed magnetic circuitIn a closed magnetic circuit, , the algebraic the algebraic sum of the product of the magnetic field strength sum of the product of the magnetic field strength and the length of each part of the circuit is and the length of each part of the circuit is equal to the resultant magnetomotive force.equal to the resultant magnetomotive force.

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Steps to solve a problem on magnetic circuit

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Air Gaps in Magnetic CircuitsAir Gaps in Magnetic CircuitsTwo purposes : Two purposes :

1.1. To permit part of a magnetic circuit to To permit part of a magnetic circuit to move, for example, in relays and in move, for example, in relays and in electrical machines.electrical machines.

2.2. To make the magnetization characteristic of To make the magnetization characteristic of the circuit more linear. the circuit more linear.

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Review Review Magnetomotive Force (MMF).Magnetomotive Force (MMF).Magnetic Field Strength (Magnetic Field Strength (HH).).Magnetic Permeability.Magnetic Permeability.Reluctance (Reluctance (RR).).Analogy between Electric and Magnetic Analogy between Electric and Magnetic Circuits.Circuits.Composite Magnetic Circuit.Composite Magnetic Circuit.Magnetic Leakage and Fringing.Magnetic Leakage and Fringing.Air Gaps in Magnetic Circuits.Air Gaps in Magnetic Circuits.