# Project Report on Transformer

### Transformer - Introduction

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__**Physics Project Report on TRANSFORMER**

**Physics Project Report on TRANSFORMER**

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Transformer - Principle:-__

A Transformer based on the Principle of mutual induction according to this principle, the amount of magnetic flux linked with a coil changing, an e.m.f is induced in the neighbouring coil.

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Construction:-__

A
transformer consists of a rectangular shaft iron core made of laminated
sheets, well insulated from one another. Two coils p_{1} & p_{2}
and s_{1} & s_{2} are wound on the same core, but are well
insulated with each other. Note that the both the coils are insulated from
the core, the source of alternating e.m.f is connected to p_{1}p_{2},
the primary coil and a load resistance R is connected to s_{1} s_{2},
the secondary coil through an open switch S. thus there can be no current
through the sec. coil so long as the switch is open.

For an ideal transformer, we assume that the resistance of the primary & secondary winding is negligible. Further, the energy loses due to magnetic the iron core is also negligible.

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INTRODUCTION OF TRANSFORMER__

__INTRODUCTION OF TRANSFORMER__

A transformer is an electrical device which is used for changing the A.C. voltages. A transformer is most widely used device in both low and high current circuit. As such transformers are built in an amazing strength of sizes. In electronic, measurement and control circuits, transformer size may be so small that it weight only a few tens of grams where as in high voltage power circuits, it may weight hundred of tones.

In a transformer, the electrical energy transfer from one circuit to another circuit takes place without the use of moving parts.

A transformer which increases the voltages is called a step-up transformer. A transformer which decreases the A.C. voltages is called a step-down transformer.

Transformer is, therefore, an essential piece of apparatus both for high and low current circuits.

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THEORY AND WORKING OF TRANSFORMER__

__THEORY AND WORKING OF TRANSFORMER__

When an altering e.m.f. is supplied to the primary coil p_{1}p_{2},
an alternating current starts falling in it. The altering current in the
primary produces a changing magnetic flux, which induces altering voltage in
the primary as well as in the secondary. In a good-transformer, whole of the
magnetic flux linked with primary is also linked with the secondary, then
the induced e.m.f. induced in each turn of the secondary is equal to that
induced in each turn of the primary. Thus if E_{p} and E_{s}
be the instantaneous values of the e.m.f.’s induced in the primary and the
secondary and N_{p} and N_{s} are the no. of turns of the
primary secondary coils of the transformer and

Dфь / d_{t} = rate of change of
flux in each turnoff the coil at this instant, we have

E_{p} = -N_{p} dфь/d_{t}
-----------------(1) And

E_{s} = -N_{s} dфь/d_{t}
----------------- (2)

Since the above relations are true at every instant, so by dividing 2 by 1, we get

E_{s} / E_{p} = - N_{s}
/ N_{p}
----------------(3)

As E_{p}
is the instantaneous value of back e.m.f induced in the primary coil p_{1},
so the instantaneous current in primary coil is due to the difference (E – E_{p}
) in the instantaneous values of the applied and back e.m.f. further if R_{p}
is the resistance o, p_{1}p_{2} coil, then the
instantaneous current Ip in the primary coil is given by

I_{p}
= E – E_{p} / R_{p}

E – E_{p} = I_{p} R_{p}

When the
resistance of the primary is small, R_{p} I_{p} can be
neglected so therefore

E – E_{p} = 0 or E_{p}
= E

Thus back e.m.f = input e.m.f

Hence equation 3 can be written as

E_{s} / E_{p} = E_{s} / E
= output e.m.f / input e.m.f = N_{s} / N_{p} = K

Where K is constant, called turn or transformation ratio.

**In a
step up transformer **

E_{s} > E so K > 1, hence N_{s}
> N_{p}

**In a
step down transformer **

E_{s} < E so K < 1, hence N_{s}
< N_{p}

If I_{p} = value of primary current at the
same instant t

And I_{s} = value of sec. current at this
instant, then

Input power at the instant t
= E_{p} I_{p} and

Output power at the same instant = E_{s}
I_{s}

If there are no losses of power in the transformer, then

Input power = output power Or

E_{p} I_{p}
= E_{s} I_{s} Or

E_{s} / E_{p}
= I_{p} / I_{s} = K

**In a
step up transformer **

As k > 1, so I_{p} > I_{s} or
I_{s} < Ip

i.e. current in sec. is weaker when secondary voltage is higher.

Hence, whatever we gain in voltage, we lose in current in the same ratio.

Similarly it can be shown, that in a step down transformer, whatever we lose in voltage, we gain in current in the same ratio.

Thus a step up transformer in reality steps down the current & a step down transformer steps up the current.

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Efficiency:-__

Efficiency of a transformer is defined as the ratio of output power to the input power. i.e.

η = output power / input power = E_{s}
I_{s} / E_{p} I_{p}

Thus in an ideal transformer, where there is no power losses, η = 1. But in actual practice, there are many power losses, therefore the efficiency of transformer is less than one.

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ENERGY LOSSES:-__

Following are the major sources of energy loss in a transformer:

1. **
Copper loss **is the energy loss in the form of heat in the copper coils
of a transformer. This is due to joule heating of conducting wires.

2. **
Iron loss **is the energy loss in the form of heat in the iron core of the
transformer. This is due to formation of eddy currents in iron core. It is
minimized by taking laminated cores.

**3.
Leakage of magnetic flux **occurs inspite of best insulations. Therefore,
rate of change of magnetic flux linked with each turn of S_{1}S_{2}
is less than the rate of change of magnetic flux linked with each turn of P_{1}P_{2}.

4. **
Hysteretic loss **is the loss of energy due to repeated magnetization and
demagnetization of the iron core when A.C. is fed to it.

5. **Magneto striation **
i.e. humming noise of a transformer.

__USES OF
TRANSFORMER__

__USES OF TRANSFORMER__

A transformer is used in almost all a.c. operations

· In voltage regulator for T.V., refrigerator, computer, air conditioner etc.

In the induction furnaces.

· A step down transformer is used for welding purposes.

· A step down transformer is used for obtaining large current.

· A step up transformer is used for the production of X-Rays and NEON advertisement.

· Transformers are used in voltage regulators and stabilized power supplies.

· Transformers are used in the transmissions of a.c. over long distances.

· Small transformers are used in Radio sets, telephones, loud speakers and electric bells etc.

__BIBLIOPGRAPHY__

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