A transformer is a static device which transfers electric power from one circuit to another by electromagnetic induction without changing the frequency in an a.c system.

There are numerous types of transformers used in various applications like audio, radio, instrument and power transformer.

**Historical background**:

In the early days, D.C systems were used for public electricity supply with the source of generation and close to the point of loading. The invention of power transformer towards the end of the nineteenth century made possible by the development of a.c supply system with generating station may located far away from load center.

For the invention of transformer, we should thankful to Mr. Faraday. In 1831 he discovered that when a changing magnetic flux links a circuit, a voltage or emf is induced in the circuit. This induced voltage is proportional to the number of turns linked by the changing flux.

If two different circuits are linked by common magnetic flux with different number of turns, there will be different voltages induced. Transformer follows this principle. In the year 1885, Hungarian engineers Karoly Zipernowsky, Otto Blathy and Miksa Deri first invented a practical transformer of some Kilovolt in primary and 100 Volt in secondary.

Today’s transformers are very much upgraded version of previous one but it still follows the same principle.

**Why transformer needed?**

Normally electric power generated in the range of 11 to 37 KV, but voltages required for domestic, commercial and industrial purposes are nearer to 230 or 400 Volt. If we transmit generation voltage from generating station to consumer, a large voltage drop as well as power losses will occur over a long distance. For economical power transmission, line to line voltage should be 0.625 KV per Km. so it is necessary to step up the sending end voltage and step down at receiving end. Several times step down may be requiring between generating station and consumer. A transformer is doing this step up and step down of voltages in an a.c circuit.

**Constructing a simple transformer:**

The transformer with its simplest form has two coils sharing a common flux.

Suppose an A.C Voltage is connected to a primary coil named coil A. Due to self induction a changing magnetic flux is induced around the coil.

Now if we placed another coil named coil B nearer to the coil A. Due to mutual induction same magnetic flux links with secondary coil (Coil B). According to the law of induction a voltage E will be induced inside the secondary coil.

Here we see that only a small portion of the total magnetic flux surrounding coil A will be linked with coil B. So, the transforming process is not very efficient. To improve the efficiency, a **magnetic circuit** is necessary which channeled the magnetic flux so that maximum flux in primary circuit can link with secondary circuit.

Now, a magnetic path becomes necessary. To fulfill this, a magnetic core surrounding the primary and secondary winding is introduced.

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**IDEAL TRANSFORMER:**

**IDEAL TRANSFORMER:**

An ideal transformer is based on certain assumptions and practically it is impossible to realize such a transformer. For understanding the transformer and to develop the mathematical model, first we visualize such a transformer.

Assumptions regarding ideal transformers are,

i) The transformer windings have no resistance, hence it has no I^{2}R loss.

ii) Transformer core material has infinite permeability so that it reduces zero m.m.f to create flux in the core.

iii) There is no magnetic leakage means there is no reactive voltage drop.

iv) Has no core loss.

Now in an ideal transformer, whose secondary is open and primary is connected with an alternating voltage, V_{1}. For this input voltage, an alternating current will flow in the primary. In case of ideal one, the primary coil is purely inductive and as there is no output, primary draws the magnetizing current I_{µ} only, which is used to magnetize the core. It is small in magnitude and lags V_{1} by 90˚. This magnetizing current produces an alternating flux ø_{1} which is in phase and proportional to the current. This alternating flux linked both with primary and secondary windings and produces self induced emf E_{1} and mutually induced emf E_{2} in secondary which is in phase with E_{1}.

This induced emf E_{1} and E_{2} at very instant equal to and in phase opposition with V_{1}, which is input primary voltage, known as **counter emf or back emf** in primary.

**E.M.F EQUATION OF TRANSFORMER**

Let N_{1}= No. of turns of transformer primary.

N_{2}= No. of turns of transformer secondary.

Ø_{m}= Maximum flux in core in weber = B_{max} X A.

f = Frequency of a.c. input in Hz.

Now, flux increases from its zero value to maximum value in one quarter of cycle, i.e. in 1/4f second.

So, average rate of change of flux = Ø_{m}/1/4f = 4f Ø_{m} Wb/s or volt.

Induced e.m.f. per turn = 4f Ø_{m} volt.

We know that Form factor = r.m.s. value/ average value = 1.11.

As flux varies sinusoidally, r.m.s. value of e.m.f. /turn = 1.11 X 4f Ø_{m} volt = 4.44f Ø_{m} volt.

For primary N_{1} turn, E_{1} = 4.44f Ø_{m}N_{1} volt.

For secondary N_{2} turn, E_{1} = 4.44f Ø_{m}N_{2} volt.

This is the e.m.f. equation of transformer. Here we see that, E_{1}/N_{1}= E_{2}/N_{2}= 4.44f Ø_{m}, that is, same e.m.f. /turn in both primary and secondary windings.

From above equation, we can write E_{2}/E_{1}= N_{2}/N_{1}=K or constant.

This ratio is called transformation ratio. If N_{2}> N_{1} i.e. K>1, then the transformer is called **step-up transformer**.

If N_{2}< N_{1} i.e. K<1, then transformer is called** step-down transformer**.

**Keep in pocket:→**

✓A transformer only transfers electric power from one circuit to another by changing the voltage and current level.

✓When energy is transformed into a higher voltage, it is known as step-up transformer, and when transformed to a lower voltage, known as step-down transformer.

✓This is a static device and cannot change the frequency level.

✓The transformer transfers electric power by means of mutual induction between two circuits linked by common magnetic flux.

✓If secondary turn is greater than primary turn, then it is step up transformer.

✓If secondary turn is lesser than primary turn, then it is step down transformer.

**Short questions related to this topic:**

Q. What does transformer transforms?

A. Power (voltage and current).

Q. A step-up transformer increases what?

A. Voltage.

Q. How transformer transforms power?

A. By linking two coil (primary & secondary) with common magnetic flux.

Q. Primary and secondary coils are linked with each other by means of?

A. Mutual induction.

Q. A transformer does not change_______?

A. Frequency.

Q. After applying primary voltage, voltage induced in secondary coil, by means of?

A. Electromagnetic induction.

Q. In case of secondary open, primary current flows____?

A. To magnetize the core .