Lecture 2 by Moeen Ghiyas Chapter 11 – Magnetic Circuits 13/08/20151.
Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas...
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Transcript of Chapter 11 – Magnetic Circuits (Part Only) Chapter 12 - Inductors Lecture 19 by Moeen Ghiyas...
Chapter 11 – Magnetic Circuits (Part Only)
Chapter 12 - Inductors
Lecture 19
by Moeen Ghiyas
19/04/23 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 2
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).
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.
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.
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).
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.
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.
19/04/23 8
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.
19/04/23 9
• 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.
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:
19/04/23 10
• where N represents the
number of turns of the coil and
dΦ/dt is the instantaneous
change in flux (in webers) linking
the coil.
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:
19/04/23 11
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.
19/04/23 12
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.)
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.
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).
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.
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.
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.
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.
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.
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.
19/04/23 21
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.
19/04/23 22
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.
19/04/23 23
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.
19/04/23 24
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
19/04/23 25
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
19/04/23 26
where Lo is the inductance of the
coil with an air core.
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.
19/04/23 27
Figures show inductor
configurations for which above
equation is appropriate.
Example – Find the inductance of the air-core coil and with
iron core μr = 2000.
Solution:
And with iron core
19/04/23 28
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
19/04/23 29
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”).
19/04/23 30
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.
19/04/23 31
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.
19/04/23 32
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
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.
19/04/23 34
Standard Values and Recognition Factor
19/04/23 35
Standard Values and Recognition Factor
19/04/23 36
Standard Values and Recognition Factor
19/04/23 37
Standard Values and Recognition Factor
19/04/23 38
Standard Values and Recognition Factor
19/04/23 39
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
19/04/23 41