INDUCTANCE
Inductance is a property of
electrical conductors, particularly
coils, that describes their ability to
oppose changes in electric
current. It's a measure of how
much a coil's magnetic field resists
changes in the current flowing
through it, thereby inducing a
voltage (electromotive force) in the
coil itself or a nearby coil. The SI
unit for inductance is the Henry
(H).
ABSTRACT
To study the factor on which the self-inductance of a
coil depends by observing the effect of this coil, when put in
series with a resistor (bulb) in a circuit fed up by an A.C. source
of adjustable frequency.
In electromagnetism and electronics, inductance is the
property of an electrical conductor by which a change in current
through it induces an electromotive force in both the conductor
itself and in any nearby conductors by mutual inductance.
These effects are derived from two fundamental
observations of physics a steady current creates a steady
magnetic field described by Oersted’s law and a time-varying
magnetic field induces an electromotive force (EMF) in nearby
conductors, which is described by Faraday’s law of induction.
According to Lenz’s law a changing electric current through a
circuit that contains inductance induces a proportional voltage,
which opposes the change in current (self-inductance). The
varying field in this circuit may also induce an EMF in
neighboring circuits (mutualinductance).
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INTRODUCTION
Self-Induction:
Self-induction is a phenomenon by which a changing
electric current produces an induced emf across the coil itself.
The ratio of induced electromotive force (EMF) across a coil to
the rate of change of current through the coil. We denote self-
inductance or coefficient of with English letter L. Its unit is
Henry (H).
Since, the induced emf (E) is proportional to the current
changing rate, we can derive an expression for the self-
inductance of a coil from Faraday’s law of electromagnetic
induction.
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VL = −N (dϕ / dt)
Where:
VL = induced voltage in volts
N = number of turns in the coil
dφ / dt = rate of change of magnetic flux in Weber’s /
second
Alternatively, the induced voltage in an inductor may
also be expressed in terms of the inductance (in henries) and the
rate of change of current.
VL = −L (di / dt)
Or
E = −L (di / dt)
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BASIC CONCEPTS
The term inductor is used to describe a circuit element
possessing the property of inductance and a coil of wire is a
very common inductor. In circuit diagrams, a coil or wire is
usually used to indicate an inductive component. Taking a
closer look at a coil will help understand the reason that a
voltage is induced in a wire carrying a changing current. The
alternating current running through the coil creates a magnetic
field in and around the coil that is increasing and
decreasing as the current changes. The magnetic field forms
concentric loops that surround the wire and join to form larger
loops that surround the coil as shown in the image below. When
the current increases in one loop the expanding magnetic field
will cut across some or all of the neighboring loops of wire,
inducing a voltage in these loops. This causes a voltage to be
induced in the coil when the current is changing.
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Basically, Lenz's law states that an induced current has a
direction such that its magnetic field opposes the change in
magnetic field that induced the current. This means that the
current induced in a conductor will oppose the change in current
that is causing the flux to change. Lenz's law is important in
understanding the property of inductive reactance, which is one
of the properties measured in eddy current testing.
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MATERIALS REQUIRED
A coil of large turns
AC source of adjustable frequency
An electrical bulb
(6V) AC ammeter of suitable range rheostat
A soft iron rod
One way key
Connecting wires
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CIRCUIT DIAGRAM
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PROCEDURE
Make all connections as shown in the circuit diagram.
Switch on the A.C. supply and adjust the constant current
in the circuit by using the variable resistor (R1) (let
frequency of source is 60 Hz and voltage is 6V).
Record the current in A.C. ammeter and see the brightness of
the bulb.
Now, put the soft iron rod inside the inductor core and record
the current in A.C. ammeter and again check the brightness of
the bulb. The current and brightness both decreases.
Now, switch off the supply and decrease the frequency of
A.C. source (say 50 Hz).
Again switch on the supply and adjust the current in
circuit at same constant voltage 6V by using the rheostat.
Note the current in ammeter and brightness of the bulb.
The current and brightness both will increase.
Again insert the iron in the core of the coil and note the current
and brightness.The current and brightness both decrease.
Repeat the steps 5, 6 and 7 for different frequencies of A.C.
source (say 40 Hz, 30 Hz and 20 Hz).
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OBSERVATION
Current in
Frequency Current in
ammeter
Of applied ammeter
with iron
S.No voltage(Hz) without iron
rod in coil
rod in coil(A)
(A)
1 60 2 1.8
2 50 2.5 2.3
3 40 2.9 2.6
4 30 3.4 3.25
5 20 4.1 4
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PRECAUTION & SOURCE OF ERROR
PRECAUTION
1. The coil should have number of turn.
2. Current should be passed for a small time to avoid the
heating effect.
3. There should not be parallax in taking the reading of
ammeter.
SOURCE OF ERROR
1. The resistance of circuit mat increase slightly due to
heating effect of current.
2. There may be eddy current in soft iron coil.
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RESULT
1. The current in the circuit decreases on inserting the iron rod in
the core of the coil at constant frequency of applied voltage and
brightness of the bulb decreases and vice-versa.
2. The current in the circuit increases on decreasing the
frequency of applied voltage and vice-versa. Therefore, the
brightness of bulb increases.
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MUTUAL INDUCTANCE
Mutual inductance can be considered as the
amount or degree of mutual induction that exists
between two coils or winding. The mutual
inductance of any two coils depends on the flux
linkage between the coils, which is turn depends
on their positions relative to each other. The
degree of flux linkage is expressed by a factor
called the coefficient of coupling. When all of
the flux lines from each coil cut, or link, the
other coil, the coefficient of coupling is 1, which
is maximum value. If only some of the flux lines
from each coil cut the other, the coefficient of
coupling has some value less than 1. You can
see then that when no mutual inductance exists
between two coils, the coefficient of coupling is
close to 1, the two coils are said to have tight
coupling; and when the value is much less than
1, the coils have loose coupling. The term
critical coupling is used to describe line between
loose the tight coupling.
When the coefficient of coupling between
two coils is known, the total inductance of the
coils is found by multiplying the values of
inductance of the coils, taking the square root of
the result, and multiplying it by the coefficient
of coupling. As an equation, this is given by:
M = k - L1 X L2
Where M is the total inductance of the
mutually coupled coils, in henrys; k is the
coefficient of coupling; and L 1 and L 2 are the
individual inductances of the coils, in henrys.
BIBLIOGRAPHY
https://www.electrical4u.com/images/2018/march18/152199894
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