The document details a physics project by Ayush Chandra, centered on measuring the impedance of an inductor with and without an iron core. It includes acknowledgments, the theoretical background of inductors, materials used, and a step-by-step procedure for constructing the inductor and conducting the experiments. The results show the total resistance and impedance values for both cases, providing a comprehensive overview of the project's findings.

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2014-2015
Ayush Chandra
XII-B
To measure impedance of an inductor with or without iron
Core

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Certificate
This is to certify that Ayush Chandra student of class XII-B and
Roll no: ___________________ of Lancers Convent School has
completed the project titled “Impedance of an Inductor with and
without iron core” during academic year 2014-2015 towards
partial fulfillment of credit for the Physics practical evaluation
of CBSE 2015 and submitted satisfactory report as compiled in
the following pages under the supervision of Ms. Nushi Jain. .

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Signature:___________________
Acknowledgement
I hereby express my gratitude to my Physics teacher
Ms.Nushi Jain for their guidance throughout my studies. Their
valuable guidance, support and supervision all through this
project are responsible for attaining the present form. I thank my
parents who supported me in all my endeavors. I also thank my
classmates who have equally worked hard to make my project a
success. And at last but not the least I thank the almighty for
whatever I have achieved till now.

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Experiment
Aim- To measure the resistance and impedance of an inductor
with or without core
APPRATUS AND MATERIAL
1. APPARATUS-A battery a high resistance rheostat, DC
Ammeter, DC Voltmeter, one way key, variable output AC
Source, AC Ammeter, AC Voltmeter, Connecting wires.
2. Material- A high resistance and large no of turns coil
wrapped on a hollow cylindrical asbestos core, a soft iron
rod fitting into the asbestos core
THEORY
An inductor, also called a coil or reactor, is a passive two
terminal electrical component which resists changes in electric
current passing through it. It consists of a conductor such as a
wire, usually wound into a coil. When a current flows through it,
energy is stored temporarily in a magnetic field in the coil.
When the current flowing through an inductor changes, the time-

5. 5
varying magnetic field induces a voltage in the conductor,
according to Faraday’s law of electromagnetic induction, which
opposes the change in current that created it. Inductance (L)
results from the magnetic field around a current-carrying
conductor; the electric current through the conductor creates a
magnetic flux. Mathematically speaking, inductance is
determined by how much magnetic flux φ through the circuit is
created by a given current i
(1)
For materials that have constant permeability with magnetic flux
(which does not include ferrous materials) L is constant and (1)
simplifies to
Any wire or other conductor will generate a magnetic field when
current flows through it, so every conductor has some
inductance. The inductance of a circuit depends on the geometry
of the current path as well as the magnetic permeability of
nearby materials. In inductors, the wire or other conductor is
shaped to increase the magnetic field. Winding the wire into a
coil increases the number of times the magnetic flux lines link
the circuit, increasing the field and thus the inductance. The
more turns, the higher the inductance. The inductance also
depends on the shape of the coil, separation of the turns, and
many other factors.
(1)ConstitutiveEQUATION

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Any change in the current through an inductor creates a
changing flux, inducing a voltage across the inductor. By
Faraday's law of induction, the voltage induced by any change in
magnetic flux through the circuit is
From (1) above
(2)
So inductance is also a measure of the amount of electromotive
force (voltage) generated for a given rate of change of current.
For example, an inductor with an inductance of 1 Henry
produces an EMF of 1 volt when the current through the
inductor changes at the rate of 1 ampere per second. This is
usually taken to be the constitutive relation (defining equation)
of the inductor.
The dual of the inductor is the capacitor, which stores energy in
an electric field rather than a magnetic field. Its current-voltage
relation is obtained by exchanging current and voltage in the
inductor equations and replacing L with the capacitance C.
(2)Lenz's law
The polarity (direction) of the induced voltage is given by
Lenz's law, which states that it will be such as to oppose the
change in current. For example, if the current through an
inductor is increasing, the induced voltage will be positive at the
terminal through which the current enters and negative at the

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terminal through which it leaves. The energy from the external
circuit necessary to overcome this potential 'hill' is stored in the
magnetic field of the inductor; the inductor is sometimes said to
be "charging". If the current is decreasing, the induced voltage
will be negative at the terminal through which the current enters.
Energy from the magnetic field is being returned to the circuit;
the inductor is said to be "discharging".
(3)Inductor construction
An inductor usually consists of a coil of conducting material,
typically insulated copper wire, wrapped around a core either of
plastic or of a ferromagnetic (or ferrimagnetic) material; the
latter is called an "iron core" inductor. The high permeability of
the ferromagnetic core increases the magnetic field and confines
it closely to the inductor, thereby increasing the inductance. Low
frequency inductors are constructed like transformers, with cores
of electrical steel laminated to prevent eddy currents. Inductors
come in many shapes. Most are constructed as enamel coated
wire (magnet wire) wrapped around a ferrite bobbin with wire
exposed on the outside, while some enclose the wire completely
in ferrite and are referred to as "shielded". Inductors used to
block very high frequencies are sometimes made by stringing a
ferrite bead on a wire. Small inductors can be etched directly
onto a printed circuit board by laying out the trace in a spiral
pattern. Some such planar inductors use a planar core. Small
value inductors can also be built on integrated circuits using the
same processes that are used to make transistors.
Procedure

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I Constructionofinductor-Using the drill bit as a template wrap
the wire, counting up to the no of turns and keep the wire
taught while turning.
1. When complete, snip off the reel at the 3cm distance from
the last turn.
2. Use some needle nosed pliers to grip the coil on the bit as
shown. Bend the legs as shown so that they are parallel.
Remove from the drill bit.
3. The legs of the coil require tinning to remove the enamel
and prime the surface for soldering onto the board.
4. Use some needle nosed pliers to grip the coil while tinning-
it can be very hot. Heat one leg with the soldering iron for a
few seconds.
5. Introduce some solder to the heated leg and continue
applying the iron moving back and forth on the leg.
6. Continue adding solder until the leg is silvered all over. You
will have to turn the coil over as you do this to ensure
coverage. Coat any surplus solder and enamel to the end of
the leg.
7. Repeat the procedure for the other leg. When complete, snip
of the ends of the legs, with the surplus solder attached,
leaving at least 1cm of straight leg before the turns.
II Measurement ofresistance

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1. Clean the ends of the connecting wires with sand paper to
remove the insulations, if any.
2. Make tight connections according to the circuit diagram.
While making connections connect the inductor to the
positive and negative ends of the battery and ensure that
positive terminals of voltmeter and ammeter are joined
towards the positive terminal of the battery.
3. Determine the least count of voltmeter an ammeter and
voltmeter are working properly.
4. Adjust the sliding contact of the rheostat such that a small
current passes through the resistance wire.
5. Note don the value of potential difference v from voltmeter
and current I from ammeter.
6. Shift the rheostat contact slightly so that both ammeter and
voltmeter show full divisions readings and not in fraction.
Iii measurementofimpedancewithoutiron core
1. Disconnect the circuit and now connect the variable ac
source is connected to AC mains, AC ammeter an AC
voltmeter are used for measuring AC current and voltage.
2. The circuit will obey ohm’s law. The ratio of the voltmeter
reading to the corresponding ammeter reading will give the
impedance of the inductor without iron core.
Iii measurementofimpedancewith iron core

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Now insert the iron core inside the hollowcylindrical
asbestos core of the inductorwith iron core.
OBSERVATION RECORD
S.no Ammeter Reading Voltmeter
Reading
R=V/I
Observed Corrected Observed Corrected
1 0.1 V 0.1 V 1.7 A 1.7 A 0.059Ω

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Measurementofresistanceandimpedance withoutiron core
Measurementofresistanceandimpedancewithiron core
S.no Ammeter Reading Voltmeter
Reading
R=V/I
Observed Corrected Observed Corrected
1 0.1 V 0.1 V 1.6 A 1.6 A 0.062Ω
2 0.1 V 0.1 V 2 A 2 A 0.05 Ω
3 0.3 V 0.3 V 4 A 4 A 0.075Ω
4 0.4 V 0.4 V 6 A 6 A 0.06 Ω
2 0.1 V 0.1 V 3 A 3 A 0.033 Ω
3 0.3 V 0.3 V 5 A 5 A 0.06 Ω
4 0.4 V 0.4 V 7 A 7 A 0.057 Ω
5 0.5 V 0.5 V 8 A 8 A 0.062 Ω
S.no (R)2 Z=(√𝑿 𝟐 + 𝒓 𝟐
(X=XL)
1 3.48 x 10-3
1.46 Ω
2 1.08 x 10-3
1.47 Ω
3 3.6 x 10-3
1.58 Ω
4 3.26 x 10-3
1.45 Ω
5 3.84 x 10-3
1.52 Ω

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5 0.5 V 0.5 V 7 A 7 A 0.07 Ω
Calculations
1.) Length of the wire=0.95 m
2.) Frequencyin India=50 Hz
1). Inductanceof L-R Circuit (L) =
𝜇𝑁2 𝐴
𝑙
=
𝜇 70 𝑋 70 𝑋 𝜋 1.7 𝑋 1.7
9.5
S.no (R)2 Z=(√𝑿 𝟐 + 𝒓 𝟐 )
(X=XL)
1 3.9 x 10-3
1.54 Ω
2 2.5 x 10-3
1.37 Ω
3 5.62 x 10-3
1.71 Ω
4 4.35 x 10-3
1.61 Ω
5 5.10 x 10-3
1.68 Ω

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=
4𝜋X10−7X 4900 X 3.14 X 2.89
9.5
=0.0558 H
2.) Inductive Reactance=XL
=2πνL
=2 x 3.14 x 50 x 0.0558
=1.758 Ω
Therefore (XL)2
=3.06 Ω
3) Mean Resistance without Iron Core=R1+R2+R3+R4+R5
=0.059+0.033+0.06+0.057+0.062
=0.054Ω
4) Mean Resistance with Iron Core=R1+R2+R3+R4+R5
=0.062+0.05+0.075+0.066+0.071
=0.064Ω
5) Mean impedance without Iron Core=Z1+Z2+Z3+Z4+Z5
=1.46+1.47+1.58+1.45+1.52Ω
=1.496 Ω
5) Mean impedance with Iron Core=Z1+Z2+Z3+Z4+Z5
=1.54+1.37+1.71+1.61+1.68
= 1.582 Ω
Result

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1.Total resistance of inductor with iron core =0.054 Ω
2.Total resistance of inductorwithout iron core =0.064 Ω
3.Total impedance of inductorwith iron core =1.496 Ω
4.Total impedance of inductorwithout iron core=1.582Ω
Bibliography

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www.wikipedia.com
 APC Physics Manual
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