The document is a physics investigatory project report on self-inductance completed by a student. It includes sections on the aim, apparatus, theory, circuit diagram, procedure, observations, result, precautions, and sources of error of the experiment. The experiment aims to study how the self-inductance of a coil depends on factors like the number of turns in the coil, geometry of the coil, and nature of the core material. The student observes changes in current and brightness of a bulb in an AC circuit when inserting an iron core into the coil and varying the frequency of the AC source.

1. NOSEGAY SENIOR
SECONDARY SCHOOL
PHYSICS
INVESTIGATORY PROJECT
SELF INDUCTANCE
ISHA SAXENA
CLASS IIX
UNDER THE GUIDANCE OF
MR.RAJAN SIR

2. CERTIFICATE
• This is to certify that ISHA SAXENA student of class
IIX has successfully completed the project file on
self inductance under the guidance of respected
MR.RAJAN SIR during the year 2022-2023
Teacher’s Signature:

3. ACKNOWLEDGMENT
• I would like to express my special thanks of gratitude to my physics
teacher MR.RAJAN SIR for his able guidance and support in
completing my project.
• I would like to extend my gratitude to the principal ma’am MRS.
SEEMA NAGPAL for providing me with all facilities that was required.
• I would now thanks my parents and friends to give this project a
creative blend and helped me in various phases of this project.

4. PROJECT OVERVIEW
• Aim
• Apparatus
• Theory
• Procedure
• Observations
• Result
• Precautions
• Source of Error

5. AIM
• 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.

6. APPARATUS
• coil of large turns
• a.c. source of adjustable frequency
• an electrical bulb
• (6V) a.c. ammeter of suitable range rheostat
• a soft iron rod
• one way key
• connecting wires

7. THEORY
• Self-inductance is the property of a coil which opposes the change in current through it. The
self inductance of a coil (long solenoid) is
• L =( μ_0 μ_r N2 A)/l
• where µr = Relative magnetic permeability of magnetic material, µr =μ/μ_0
• N =Total number of turns in solenoid
• A = Area of cross-section of solenoid
• l = Length of solenoid
• Hence, the self inductance depends upon
• No. of turns in solenoid

8. • Geometry of coil, L A , L 1/l
• Nature of core material, L µ
• When an inductor is connected in series with a resistor (bulb) with a variable source of
frequency , then current flowing in the bulb is
• Irms = E_rms/Z
• where Z =√(R2 )+ ω2 L2 = Impedance of the a.c. circuit
• Here R = Resistance of bulb
• L = Self inductance of coil
• ω = 2πf = Angular frequency of a.c. source.
• The brightness of bulb i.e., Heat generated in bulb is
• H = I_rme2 Zt
• P = H/t = Irms
2 Zt
• P = Irms
2 √R2 + ω2 L2

9. CIRCUIT DIAGRAM

10. PROCEDURE
• • Make all connections as shown in 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 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 bulb. The current and brightness both
decreases.

11. • 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 bulb. The current and
brightness both will increases.
• Again insert the iron in the core of coil and note the current and brightness. The current
and brightness both decreases.
• Repeat the steps 5, 6 and 7 for different frequency of A.C. source(say 40 Hz,30 Hz and 20
Hz).

12. OBSERVATION
• 1. Least count of ammeter = .......... A
• 2. Zero error of ammeter= ............. A
• 3. Range of ammeter= ....................A

13. RESULT
• 1. The current in the circuit decrease on inserting the iron rod in the
core of coil at constant frequent of applied voltage and brightness of
bulb decrease and vice-versa.
• 2. The current in the circuit increase on decreasing the frequency of
applied voltage and vice-versa. Therefore, the brightness of bulb
increase.

14. PRECAUTIONS
• 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.

15. 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.
• 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 (mutual inductance).

16. The term inductance was coined by Oliver Heaviside in 1886. It is customary to use the symbol L for
inductance, in honors of the physicist Heinrich Lenz in the SI system, the measurement unit for inductance
is the Henry, with the unit symbol H, named in honor of Joseph Henry who discovered inductance
independently of, but not before, Faraday.
Lenz's law named after the physicist Heinrich Lenz who formulated it in 1834, says:
The direction of current induced in a conductor by a changing magnetic field due to Faraday’s law of
induction will be such that it will create a field that opposes the change that produced it.

17. Lenz's law is shown by the negative sign in Faraday’s law of induction:-
which indicates that the induced voltage and the change in magnetic flux have
opposite signs. It is a qualitative law that specifies the direction of induced current
but says nothing about its magnitude. Lenz's Law explains the direction of many
effects in electromagnetism, such as the direction of voltage induced in an inductor
or wire loop by a changing current, or why eddy currents exert a drag force on
moving objects in a magnetic field.
Lenz's law can be seen as analogous to Newton’s third law in classic mechanics.
For a rigorous mathematical treatment, see electromagnetic induction and
Maxwell’s equations.
Inductors do this by generating a self-induced emf within itself as a result of their
changing magnetic field. In an electrical circuit, when the emf is induced in the
same circuit in which the current is changing this effect is called Self-induction, ( L )
but it is sometimes commonly called back-emf as its polarity is in the opposite
direction to the applied voltage.

18. When the emf is induced into an adjacent component situated within the same magnetic field,
the emf is said to be induced by -induction, (M) and mutual induction is the basic operating
principal of transformers, motors, relays etc. Self inductance is a special case of mutual
inductance, and because it is produced within a single isolated circuit we generally call self-
inductance simply, Inductance.
The basic unit of measurement for inductance is called the Henry, (H) after Joseph Henry, but
it also has the units of Webers per Ampere ( 1 H = 1 Wb/A ).
Lenz’s Law tells us that an induced emf generates a current in a direction which opposes the
change in flux which caused the emf in the first place, the principal of action and reaction.
Then we can accurately define Inductance as being: “a coil will have an inductance value of
one Henry when an emf of one volt is induced in the coil were the current flowing through the
said coil changes at a rate of one ampere/second”.
In other words, a coil has an inductance, ( L ) of one Henry, ( 1H ) when the current flowing
through it changes at a rate of one ampere/second, ( A/s ) inducing a voltage of one volt, ( VL
) in it.

19. This mathematical representation of the rate of change in current through a coil per unit time is
given as:
di/dt (A/s)
Where: di is the change in the current in Amperes and dt is the time taken for this current change in
seconds. Then the voltage induced in a coil, ( VL ) with an inductance of L Henries as a result of
this change in current is expressed as:
VL = -L di/dt (V)
Note that the negative sign indicates that voltage induced opposes the change in current through
the coil per unit time (di/dt).

20. BIBLIOGRAPHY
• www.google.com
• Lab manual of physics S.L Arora
• NCERT of physics

21. THANK YOU