Question 9: What is transformer? Give its principle, mathematical relationship. Also explain why laminated iron core is used instead of solid iron?

## Transformer

The device which increases or decreases the value of alternating voltage is called transformer.

## Principle

The principle of transformer is based on the phenomenon of mutual induction. There are two coils in the transformer. Changing current in one induces an emf in the other.

## Construction

A transformer has three major parts; (1) primary coil (2) secondary coil (3) laminated iron core. Both coils are wound on the iron core. The coil connected to the input alternating current is called primary coil and the coil connected to the output voltage is called secondary coil. The alternating current through the primary coil creates a changing magnetic field resulting in a changing magnetic flux. The changing magnetic flux induces an emf across the ends of the secondary coil.

## Mathematical Relation

When an alternating voltage is applied to the primary coil, an alternating current sets up in it. This current produces a continuous changing magnetic flux (Faraday’s Law). The changing flux links the secondary coil and induces an emf in it (phenomenon of mutual induction). The magnitude of the induced emf in the secondary coil depends upon the number of turns in the primary and secondary coils.

Let Vp is the applied voltage to the primary coil and Np is the number of turns in it, then according to the Faraday’s law of electromagnetic induction,

In the same way, for the secondary coil,

Divide (2) by (1)

This is the basic mathematical relationship for the working of a transformer.

Based on this relationship, we can have two types of transformers.

#### (1) Step-up transformer

Have a look of equation (Z) once more. If we decrease the number of turns in the primary coil, the ratio (quotient) will increase. Being equality, the LHS will also increase. But increase in the LHS means increase in the secondary voltage Vs. Therefore, if we decrease the number of turns in the primary coil, the secondary voltage will increase. Such a transformer in which the primary voltage is less than the secondary voltage is called a step-up transformer.

#### (2) Step-down transformer

Again by equation (Z), the secondary voltage will be less than the primary voltage if the number of turns in the primary coil (Np) is greater than the number of turns in the secondary coil. Such a transformer in which the out-put voltage is less than the input voltage is called a step-down transformer.

#### Efficiency consideration in a transformer

Transformer is a good machine with efficiency in the range of 90%.

In a transformer, electric power is transferred from the primary coil to the secondary due to the changing flux. A sophisticated construction of the transformer makes a little wastage of flux and the flux linking both the primary and secondary coils is almost the same. So for a theoretically ideal transformer,

Here Ip and Is are currents flowing in the primary and secondary coils respectively. These shows the currents are inversely proportional to the respective voltages in their own coils. Hence, when the voltage is stepped up, the current is stepped down and when voltage is stepped down the current is stepped up. Therefore for a high voltage a stepped up transformer is used and for a high current a stepped down transformer is used.

#### Uses of transformer

• Perhaps the most important use is in the transmission and distribution of electric power. From the generation plant, electric power is transferred in high voltage and low current. This saves losses due to the heating effect by the flow of current. When current is distributed for the use in the households or industries, a step down transformer is used.
• It is used in the design of various electric circuits for communication purposes like in radios and televisions etc.

### Reason for using laminated iron core

Iron core of a transformer is made of laminated iron. Lamination is the technique of making the core with multiple thin sheets (called lamina) of iron pressed together with a thin film of insulation (glue) between the sheets.

Why we do this?

Iron has high permeability. Due to this property it is used as core in the transformer.  Most of the diverging magnetic lines of force from the primary coil are also attracted towards the iron core which then passes through the secondary coil as well and the flux leakage is controlled.

However, being a conducting loop, it also experiences a changing magnetic flux with the whole assembly of the transformer. Naturally current is induced in it. Such currents are called eddy current. But iron core is designed for the magnetic field and not for the current. Such currents are unwanted for the reason it causes loss of energy by heating the iron core (since power dissipated is proportional to the square of the current). More current will lose more energy. Therefore it is essential to reduce the eddy current.

Thus transformer is made of laminated iron instead one bulk of iron. Since the current is confined to a single lamina by the insulating material and the cross-section of the lamina is very small. Therefore, less current is produced and the energy dissipation due to eddy currents is controlled. This should be noted that the sum of currents in all lamina is also less than the case if the core was made of one single bulk of iron.