Investigatory Project Physics made by crimemaster gogo in academic session 2022-23 Do not blatantly copy this content inspirations are allowed other wise strict legal action will be taken against the party comiting the act the picture quality has been diminished due to this stupid platform but if you need higher quality Pdf contact : crimemastergogo342@gmail.com

1. 1
Certificate
This is to certify that Master Rudraksha Dwivedi, a
student of class 12th
has successfully completed the
research on the below mentioned project under the
guidance of __________________ during the year 2022-23
in partial fulfilment of Physics Practical Examination
conducted by AISSCE, New Delhi.
Signature of Physics Teacher Signature of External Examiner
Signature of Principal School Stamp

2. 2
Acknowledgment
In the accomplishment of this project successfully, many people
have best owned upon me their blessings and the heart pledged
support, this time I am utilizing to thank all the people who have
been concerned with project.
Primarily I would like to thank my Physics Teacher
Mrs. Sujata Ghodke
whose valuable guidance has been the ones that helped me patch
this project and make it full proof success her suggestions and her
instructions has served as the major contributor towards the
completion of this project.
Then I would like to thank my parents and Classmates who have
helped me with their valuable suggestions and guidance has been
helpful in various phases of the completion of the project.

3. 3
Index
Section Page Number
1. Introduction
2. Discovery of Induction
3. Mutual Induction
4. Mutual Induction in coaxial coils
5. Basic Construction
6. Mathematical Description
7. Types of Transformers
8. Types of power losses
9. Efficiency of a Transformer
10. Bibliography

4. 4
Introduction
A passive component that transfers electrical energy from one electrical
circuit to another circuit, or multiple circuits
--Also known as --
Transformer
But what is the use of this instrument?
Transformers are employed for widely varying purposes; e.g., to reduce the
voltage of conventional power circuits to operate low-voltage devices, such as
doorbells and electric/diesel operated locomotive trains, and to raise the
voltage from electric generators so that electric power can be transmitted over
long distances.
“Why do power losses happen?”
Since most of the power plants are far from residential dwellings, there needs
to be a strategic way to distribute power. The first step of transmission
involved the use of high-voltage lines that transmit the electricity long
distance. The reason that high voltage is used is that it helps in keeping the
power losses low.
Since now we know that we need to use high potential lines to transfer power
we need to step up and step down this potential/ voltage accordingly
This is exactly where a transformer comes into play.
The Transformer will step up or step down the voltages according to our needs
Now, lets have look in the actual working principles and construction of the
transformer.

5. 5
Aim:
To make a scale step UP/DOWN Transformer
Materials required:
Steel flat bar, 4 pieces
Miscellaneous bolts, nuts, washers
28 gauge “magnet” wire
Low-voltage AC power supply
Circuit Diagram of a Transformer :

6. 6
Theory:
Discovery of induction
Electromagnetic induction, the principle of the operation of the
transformer, was discovered independently by Michael Faraday
in 1831 and Joseph Henry in 1832.
Only Faraday furthered his experiments to the point of working
out the equation describing the relationship between EMF and
magnetic flux now known as Faraday's law of induction:
|𝜀| = |
ⅆ𝜙
ⅆ𝑡
|…………………………………………………………[1]
Where |𝜀| denotes the magnitude of EMF generated by the
rate of change of magnetic flux
However, a modification to this expression called Lenz’s law
states that:
The current induced in a circuit due to a change in a magnetic
field is directed to oppose the change in flux and to exert a
mechanical force which opposes the motion.
This can be expressed as:
ϵ = −N
∂ϕ
∂t
Mutual Induction
When two coils are brought in proximity with each other the
magnetic field in one of the coils tend to link with the other. This
further leads to the generation of voltage in the second coil.

7. 7
This property of a coil which affects or changes the current and
voltage in a secondary coil is called mutual inductance.
Mutual Inductance of a Coaxial Solenoid:
Consider two coaxial solenoids of which the outer solenoid S2
has radius r2 and N2 turns whereas the inner solenoid S1 has
radius r1 and N1 turns. Both the solenoids are of equal length.
When there is a current I2 in the solenoid S2, the magnetic
induction due to I2 is given by,
The corresponding flux linkage with solenoid S1 is,
𝐍𝟏𝛟 = 𝐌𝟏𝟐𝐈𝟐
N1 is called the mutual inductance of solenoid S1 with respect to
solenoid S2. It is also referred to as the coefficient of mutual
induction. For these simple co-axial solenoids it is possible to
calculate M12. The magnetic field due to the current I2 in S2 is
𝑈0𝜂2𝐼2 The resulting flux linkage with coil S1 is,
𝐍𝟏𝛟𝟏 = 𝐧𝟏𝐥𝛑𝐑𝟏
𝟐
𝛍𝟎𝐧𝟐𝐈𝟐
= 𝐮𝟎𝐧𝟏𝐧𝟐𝛑𝐑𝟏
𝟐
𝐥𝐈𝟐
Now,
𝐌𝟏𝟐 = 𝐮𝟎𝐧𝟏𝐧𝟐𝛑𝐑𝟐
𝟐
𝐥

8. 8
Note that we neglected the edge effects and considered the
magnetic field μ0n2I2 to be uniform throughout the length and
width of the solenoid S2. This is a good approximation keeping
in mind that the solenoid is long, implying l >> r2
We now consider the reverse case. A current I1 is passed
through the solenoid S1 and the flux linkage with
coil S2 is
𝐍𝟐𝛟𝟐 = 𝐌𝟐𝟏𝐈𝟏
Where M21 is the mutual inductance of solenoid 2 w.r.t.
solenoid 1
𝐍𝟐𝛟𝟐 = 𝐧𝟐𝐥𝛑𝐑𝟏
𝟐
𝛍𝟎𝐧𝟏𝐈𝟏
𝑴𝟐𝟏 = 𝝁𝟎𝒏𝟏𝒏𝟐𝝅𝑹𝟏
𝟐
𝒍
Let, M21=M12=M
if a medium of relative permeability μR had been present, the
mutual inductance would be:
𝐌 = 𝛍𝐑𝐮𝟎𝐧𝟏𝐧𝟐𝛑𝐑𝟏
𝟐
𝐥
Basic construction of transformer
Basically a transformer consists of two inductive windings and a
laminated steel core. The coils are insulated
from each other as well as from the steel core. A transformer
may also consist of a container for winding and
core assembly (called as tank), suitable bushings to take our
the terminals, oil conservator to provide oil in the
transformer tank for cooling purposes etc. The figure at left
illustrates the basic construction of a transformer.

9. 9
In all types of transformers, core is constructed by assembling
(stacking) laminated sheets of steel, with
minimum air-gap between them (to achieve continuous
magnetic path). The steel used is having high silicon
content and sometimes heat treated, to provide high
permeability and low hysteresis loss. Laminated sheets of
steel are used to reduce eddy current loss. The sheets are cut
in the shape as E,I and L. To avoid high reluctance
at joints, laminations are stacked by alternating the sides of
joint. That is, if joints of first sheet assembly are at
front face, the joints of following assemble are kept at back face
Fig1 :.Schematic Diagram of the transformer
Fig2 :.Transformer for distributing power to common house
holds

10. 10
Fig3 :.Schematic Diagram of a commercial transformer
Fig4 :.Commercial Transformers used in power distribution
stations

11. 11
Mathematical description:
For an ideal transformer, we consider that resistances of the
primary and secondary coils are negligible. Let the E.M.F. of
the alternate current supplied by the A.C source be
EP=E0Sin(ωt)
Let’s assume that the primary winding to be a pure inductance,
so here Ip will lag behind the voltage EP by 900.
Thus the power factor for primary coil becomes,
Cos(ϕ)=Cos(Pi/2)=0.
Let that the number of turns in primary wire be NP and
secondary wire be NS
According to faraday law, the induced E.M.F. through one turn
of both the coils will be the same.
Let the flux through one turn be ϕ, the flux through the primary
coil be ϕp and the flux through the secondary coil be ϕs.
So,
𝜙1 = 𝑁𝑝𝜙
𝜙2 = 𝑁𝑠𝜙

12. 12
We also know by Faraday’s law [1].
𝜖 = −𝑁
𝜕𝜙
𝜕𝑡
So for the primary coil this Eqn
can be modified as :
𝛆𝐩 =
𝛛𝛟𝐩
𝛛𝐭
And for secondary coil :
𝛆𝐬 =
𝛛𝛟𝐬
𝛛𝐭
On dividing these equations:
𝜀𝑠
𝜀𝑝
=
𝜕𝜙𝑆 =
𝜕𝜙𝑝
𝑁𝑠
𝑁𝑝
𝜙
𝜙
𝜺𝒔 = 𝜺𝑷
𝑵𝒔
𝑵𝒑
Apart from this If we consider the transformer to be ideal
Then the Power (IN) = Power (OUT)
Since P=VI
PP=EP IP
Ps=Es Is
If Pp=Ps
EP IP= Es Is
𝛆𝐩
𝛆𝐬
=
𝐍𝐩
𝐍𝐒
=
𝐢𝐬
𝐢𝐩
𝑰𝒔 = 𝑰𝒑
𝑵𝒑
𝑵𝒔
Valid for an Ideal transformer only with no losses.

13. 13
Types of Transformers
1. Step-up Transformer
Considered a step-up transformer shown in the figure below. The E1
and E2 are the voltages, and T1 and T2 are the number of turns on
the primary and secondary winding of the transformer.
A transformer in which the output (secondary) voltage is greater than
its input (primary) voltage is called a step-up transformer. The step-up
transformer decreases the output current for keeping the input and
output power of the system equal.

14. 14
The number of turns on the secondary of the transformer is greater
than that of the primary, i.e., T2 > T1.Thus the voltage turn ratio of the
step-up transformer is 1:2. The primary winding of the step-up
transformer is made up of thick insulated copper wire because the
low magnitude current flows through it.
εo > εi
ε0
εi
< 1
𝐍𝐬
𝐍𝐏
< 𝟏
2.Step-Down Transformer
A transformer in which the output (secondary) voltage is less than its
input (primary) voltage is called a step-down transformer. The number of
turns on the primary of the transformer is greater than the turn on the
secondary of the transformer, i.e., T2 < T1. The step-down transformer
is shown in the figure below
The voltage turn ratio of the step-down transformer is 2:1. The voltage
turn ratio determines the magnitude of voltage transforms from primary
to secondary windings of the transformer.
Step-down transformer is made up of two or more coil wound on the iron
core of the transformer. It works on the principle of magnetic induction
between the coils. The voltage applied to the primary of the coil

15. 15
magnetise the iron core which induces the secondary windings of the
transformer. Thus the voltage transforms from primary to the secondary
winding of the transformer.
εo > εi
ε0
εi
> 1
𝐍𝐬
𝐍𝐏
> 𝟏
Types of power Losses in a real transformer
and
Methods of Preventions
1. Hysteresis Loss:
The repeated magnetisation and demagnetisation of the iron core
caused by the alternating input current, produces loss in energy called
hysteresis loss. This loss can be minimised by using a core with a
material having the least hysteresis loss. Alloys like Mu-metal and silicon
steel are used to reduce hysteresis loss.
2. Eddy current loss:
In the transformer, A.C is provided to the primary side which determines
the alternating magnetizing flux. Once this flux links with the secondary
side, it generates induced EMF in it. But some components of this flux
also get linked with other conducting sections like iron body or steel
core or the transformer, which will produce induced EMF in those parts,
causing small flowing current in them. This current is introduced as eddy
current. Because of these eddy currents, some power will be dissipated in
the form of heat.

16. 16
3. Flux Loss:
The flux produced in the primary coil is not completely linked with the
secondary coil due to leakage. This results in the loss of energy. This
loss can be minimised by using a shell type core. In addition to the
above losses, due to the vibration of the core, sound is produced, which
causes a loss in the energy.
4. Heating Loss:
The current flowing through the primary and secondary windings lead to
Joule heating effect. Hence some energy is lost in the form of heat.
Thick wires with considerably low resistance are used to minimise this
loss.
Efficiency of Transformer
The efficiency of transformer is defined as the ratio of output
power to input power. It is denoted by (η)
As the output power is always less than the input power due to
losses in the transformer, practically the transformer efficiency
is always between 0 and 1 i.e. 0% and 100% but it can never
be 1 (i.e.100%).
The efficiency of an ideal transformer is equal to 1 or 100%
since the losses in the ideal transformer are zero.
Fig5 :.Efficiency vs Output power

17. 17
The graph of output power versus efficiency of transformer is
shown in the figure. The figure shows that the efficiency
increases with the increase in the output power up to a certain
value and after a particular value of output power, the
transformer efficiency decreases.
Efficiency of Transformer | Formula
𝜼 =
𝑶𝒖𝒕𝒑𝒖𝒕 𝑷𝒐𝒘𝒆𝒓
𝑰𝒏𝒑𝒖𝒕 𝑷𝒐𝒘𝒆𝒓
𝜼 =
𝑶𝒖𝒕𝒑𝒖𝒕 𝑷𝒐𝒘𝒆𝒓
𝑶𝒖𝒕𝒑𝒖𝒕 𝑷𝒐𝒘𝒆𝒓 + 𝑳𝒐𝒔𝒔𝒆𝒔
η =
𝒗𝟐𝑰𝟐 𝐜𝐨𝐬 𝝓𝟐
𝒗𝟐𝑰𝟐
𝐜𝐨𝐬 𝝓𝟐 + 𝒑𝑯 + 𝒑𝒉
Where, PH is the Hysteresis loss + Eddy Currents
Ph is the Heating loss
𝐜𝐨𝐬 𝝓𝟐 is the load power factor
Fig6 :. Hysteresis loss curve between B vs H

18. 18
To minimise hysteresis we use a material that has low
hysteresis loss that is the material with low coercivity and low
retention
The area is directly proportional to the magnitude of loss by the
hysteresis per cycle per unit volume.
As such we use silicon steel (from the graph) for the lamination
of the core of the transformer.
Procedure
Wrap two, equal-length bars of steel with a thin layer of
electrically-insulating tape. Wrap several hundred turns of
magnet wire around these two bars. You may make these
windings with an equal or unequal number of turns, depending
on whether or not you want the transformer to be able to “step”
voltage up or down.
Applications of Transformers:
Power Transformers: These kinds of transformers are used for
high voltage power transfer applications (more than 33 KV).
They are usually bigger in size and can occupy larger space.
Distribution Transformers: These type of transformers are used
to distribute the generated power to distant locations. It is used
for distributing electricity at low voltage that is less than 33 KV
in industry or 220-440 V for household purposes.

19. 19
Measurement Transformers: This kind of uses of transformer
helps in measuring voltage, current, and power, etc.
According to the place of use, transformers are classified into:
Indoor Transformers: These are covered with roofs and
shelters just like the industry types.
Outdoor Transformers: These are mainly kept outside and are
used as distribution type transformers.
While performing a manufacturing process, chemical
engineering like electrolysis and electroplating is usually fueled
by a regulated flow of current which is supplied with the help of
a transformer. The current flow can be regulated according to
the reaction.
During steel manufacturing process, high currents are required
for melting and welding of steel and lower currents are required
for cooling. Transformers provide a well regulated current
during all these processes.
Transformers are also used for battery charging process. The
voltage has to be controlled properly for not causing any
damage to internal battery components which can be done only
with the help of a transformer.

20. 20
Precautions :
1. Do not use high voltage to make the transformer
2. Do not touch the copper winding or the iron block while
the transformer is in operation.
Sources of Error :
1. Values of the current might change due to copper losses
(Heating losses).
2. Eddy Current can change the readings.

21. 21
Session 2022-23
Physics Investigatory project
Topic: “Transformers”
Roll No.: __________
Submitted To: _________
Submitted By: Rudraksha Dwivedi
Class: 12th
Section: A

22. 22
Bibliography
1. NCERT text book for Physics Class 12
2. NCERT Physics lab manual
3. https://www.britannica.com/
4. https://www.electrical4u.com/
5. www.lucidcharts.com
6. https://paperswithcode.com/method/transformer