Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas...

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Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 16/06/22 1

Transcript of Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas...

Page 1: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Chapter 11 – Magnetic Circuits (Part Only)

Chapter 12 - Inductors

Lecture 19

by Moeen Ghiyas

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Page 2: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Magnetic Fields – Ch 11

Introduction to Inductors

Faraday’s Law of Electromagnetic Induction

Lenz’s Law (& Magnetic Field, Permeability – Ch 11)

Permeability (μ) – Ch 11

Self Induction

Types of Inductors

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In the region surrounding a permanent magnet there exists a

magnetic field, which can be represented by magnetic flux lines

Flux in dictionary – fluctuation, change, unrest

Magnetic flux lines, do not have origins or terminating points and

exist in continuous loops and radiate from north to south pole

returning to the north pole through the metallic bar

Symbol for magnetic flux is the Greek letter Φ (phi).

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Magnetic flux line will occupy as small an area as possible, which

results in magnetic flux lines of minimum length between the poles.

The strength of a magnetic field in a particular region is directly

related to the density of flux lines.

In fig, the magnetic field strength at a is twice than at b since twice as

many magnetic flux lines are associated with the perpendicular plane

at a than at b.

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If unlike poles of two permanent magnets are brought together, the

magnets will attract, and the flux distribution will be as shown in

Fig 11.2.

If like poles are brought together, the magnets will repel, and the

flux distribution will be as shown in Fig. 11.3.

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If a nonmagnetic material, such as glass or copper, is

placed in the flux paths surrounding a permanent

magnet, there will be an almost unnoticeable change in

the flux distribution (Fig. 11.4).

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If a magnetic material, such as soft iron, is placed in the flux path, the

flux lines will pass through the soft iron with greater ease through

magnetic materials than through air.

Above principle is used in the shielding of sensitive electrical

elements / instruments that can be affected by stray magnetic fields.

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we shall consider a third element, the inductor, which has a

number of response characteristics similar in many respects

to those of the capacitor.

Inductors are coils of various dimensions designed to

introduce specified amounts of inductance into a circuit.

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If a conductor is moved through a magnetic field so that it cuts

magnetic lines of flux, a voltage will be induced across conductor.

The greater the number of flux lines cut per unit time (by increasing

speed), or stronger the magnetic field strength (for same traversing

speed), the greater will be the induced voltage across the conductor.

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• or if the conductor is held

fixed and the magnetic field is

moved so that its flux lines cut

the conductor, the same effect

will be produced.

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If a coil of N turns is placed in the region of a changing flux,

as in fig, a voltage will be induced across the coil as:

Faraday’s law:

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• where N represents the

number of turns of the coil and

dΦ/dt is the instantaneous

change in flux (in webers) linking

the coil.

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The term linking refers to the flux within the turns of wire.

The term changing simply indicates if the flux linking the coil

ceases to change, such as when the coil simply sits still in a

magnetic field of fixed strength, dΦ/dt = 0, and the induced

voltage e = N(dΦ/dt) = N(0) = 0.

. Faraday’s law:

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Lenz’s law, states that an induced effect is always such

as to oppose the cause that produced it.

But to understand it we need to study magnetic field and

its relationship with current.

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A magnetic field (represented by concentric flux lines) is present

around every wire carrying electric current.

The direction of the magnetic flux lines can be found simply by

placing the thumb of the right hand in the direction of

conventional current flow and noting the direction of the fingers.

(Called as right-hand rule.)

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If the conductor is wound in a single-turn coil , the resulting flux

will flow in a common direction through the centre of the coil.

A coil of more than one turn would produce a magnetic field in a

continuous path through and around the coil (Fig. 11.8).

The flux lines leaving the coil from the left and entering to the right

simulate a north and a south pole, respectively.

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Flux distribution or field strength of coil is quite similar to but

weaker than a permanent magnet. However, it can be effectively

increased by placing a core of certain materials, (iron, steel, or

cobalt, etc) within the coil to increase the flux density within coil.

With the addition of a core, we have devised an electromagnet

whose field strength can be varied by changing one of the

component values (current, turns, and so on).

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For same physical dimensions, strength of the

electromagnet will vary in accordance with the material

of core used. This variation in strength is due to the

greater or lesser number of flux lines passing through

the core.

Materials in which flux lines can readily be set up are

said to be magnetic and to have high permeability.

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The permeability (μ) of a material, therefore, is a

measure of the ease with which magnetic flux lines can

be established in the material. It is similar to conductivity

in electric circuits. The permeability of free space μo

(vacuum) is

Practically speaking, the permeability of all non-

magnetic materials, such as copper, aluminium, wood,

glass, and air, is the same as that for free space.

Page 18: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Materials that have permeability slightly less than that of

free space are said to be diamagnetic,

Those with permeability slightly greater than that of free

space are said to be paramagnetic.

Magnetic materials, such as iron, nickel, steel, cobalt,

and alloys of these metals, have permeability hundreds

and even thousands of times that of free space.

Materials with these very high permeability are referred

to as ferromagnetic.

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The ratio of the permeability of a material to that of free

space is called its relative permeability μr ; that is,

In general, for ferromagnetic materials, μr ≥ 100, and for

nonmagnetic materials, μr = 1.

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The direction of flux lines can be determined for the

electromagnet by placing the fingers of the right hand in

the direction of current flow around the core. The thumb

will then point in the direction of the north pole of the

induced magnetic flux.

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We now know from magnetic circuits that if the current

increases in magnitude, the flux linking the coil also

increases.

However, only a changing flux linking a coil induces a

voltage across the coil.

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For this coil, therefore, an induced voltage is developed

across the coil due to the change in current through the coil.

The polarity of this induced voltage (eind) tends to

establish a current in the coil that produces a flux that

will oppose any change in the original flux.

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The instant the current begins to increase in magnitude, there will

be an opposing effect trying to limit the change. It is “choking” the

change in current through the coil. Hence, the term choke is often

applied to the inductor or coil.

Thus Lenz’s law, states that an induced effect is always such

as to oppose the cause that produced it.

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Page 24: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

This ability of a coil (Lenz’s Law) to oppose any change in

current is a measure of the self-inductance L of the coil. For

brevity, prefix self is usually dropped. Inductance is measured

in henries (H), after the American physicist Joseph Henry.

Inductors are coils of various dimensions designed to

introduce specified amounts of inductance into a circuit.

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Page 25: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

The inductance of a coil varies directly with the magnetic

properties of the coil.

Ferromagnetic materials, therefore, are frequently employed

to increase the inductance by increasing flux linking the coil.

A close approximation can be found by

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Page 26: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

where N represents the number of turns; μ, the permeability

of the core (note that μ is not a constant and depends on

other magnetizing parameters); A, the area of the core in

square meters; and ℓ is the mean length of core in meters.

Substituting μ = μr μo ;

. And thus

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where Lo is the inductance of the

coil with an air core.

Page 27: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Equations for the inductance of

coils different from those shown

above can be found in reference

handbooks. Most of the equations

are more complex than just

described.

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Figures show inductor

configurations for which above

equation is appropriate.

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Example – Find the inductance of the air-core coil and with

iron core μr = 2000.

Solution:

And with iron core

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Page 29: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Practical Equivalence

Inductors, like capacitors, are not ideal.

Every inductor has a resistance equal to resistance of turns

and a stray capacitance due to the capacitance between the

turns of the coil.

However, stray capacitance can be ignored, resulting in the

equivalent model

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Page 30: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Practical Equivalence

For most applications, we have been able to treat the

capacitor as an ideal element and maintain a high degree of

accuracy.

For the inductor, however, RL must often be included in the

analysis and can have a pronounced effect on the response

of a system (Chapter 20, “Resonance”).

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Page 31: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Practical Equivalence

The level of RL can extend from a few ohms to a few hundred

ohms.

Note that the longer or thinner the wire used in the construction of

the inductor, the greater will be the dc resistance as determined

by R = ρl /A.

However, in our initial analysis we will treat the inductor as an

ideal element.

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Page 32: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Symbols

Appearance

Fixed Inductor: The fixed air-core and iron-core inductors already

discussed.

Variable Inductor: The permeability-tuned variable coil has a

ferromagnetic shaft that can be moved within the coil to vary the

flux linkages of the coil and thereby its inductance.

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Page 33: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Testing

The primary reasons for inductor failure are shorts that develop between

the windings and open circuits in the windings due to factors such as

excessive currents, overheating, and age.

The open-circuit condition can be checked easily with an ohmmeter (∞

ohms indication), but the short-circuit condition is harder to check

because the resistance of many good inductors is relatively small.

A short between the windings and the core can be checked by simply

placing one lead of the meter on one wire (terminal) and the other on the

core itself. An indication of zero ohms reflects a short between the two

because the wire that makes up the winding has an insulation jacket

throughout. 19/04/23 33

LCR meter

Page 34: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Standard Values and Recognition Factor

Like the capacitor, the most common employ the same

numerical multipliers / tolerances as the most common

resistors.

In general, therefore, we find inductors with the following

multipliers: 0.1 μH, 0.12 μ H, 0.15 μ H, 0.18 μ H, 0.22 μ H,

0.27 μ H, 0.33 μ H, 0.39 μ H, 0.47 μ H, 0.56 μ H, 0.68 μH,

and 0.82 μ H, and then 1 mH, 1.2 mH, 1.5 mH, 1.8 mH, 2.2

mH, 2.7 mH, and so on.

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Standard Values and Recognition Factor

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Standard Values and Recognition Factor

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Standard Values and Recognition Factor

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Standard Values and Recognition Factor

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Page 39: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Standard Values and Recognition Factor

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Page 40: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

Magnetic Fields – Ch 11

Introduction to Inductors

Faraday’s Law of Electromagnetic Induction

Lenz’s Law (& Magnetic Field, Permeability – Ch 11)

Permeability (μ) – Ch 11

Self Induction

Types of Inductors

19/04/23 40

Page 41: Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas 06/08/2015 1.

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