Transformer: Check Working Principle, Definition, Types & Class 12 Notes

We can define a transformer as an electrical device that transforms the AC voltage without changing its frequency. It works on the principle of mutual induction. There are mainly two types of transformers: step-up transformers and step-down transformers.

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To construct a transformer, we need a laminated iron core and a copper wire. Moreover, insulation and cooling systems are also integral to ensure safe and efficient operation. Let's discuss the components of a transformer below:

Core

Earlier, an iron core was used in a transformer. Now in modern transformers, we use laminated silicon steel cores, because they reduce the energy loss, such as hysteresis loss and eddy current loss. The silicon steel minimizes the energy loss and provides a path for magnetic flux. The shape of the core is E-I or toroidal.

Copper Wire

There are two sets of wires in a transformer: primary and secondary. We use copper wire because it is a good conductor of electricity. The wire is wound around the iron core.
The primary winding is connected to the input voltage source, and the secondary winding is connected to the output.

When current passes through the primary coil, a magnetic field is produced in the core. The magnetic field generates a voltage in the secondary winding.

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A transformer works on the principle of mutual induction of two coils or Faraday’s Law of Electromagnetic induction. When the current in the primary coil is changed, the flux linked to the secondary coil also changes. Hence, an EMF is induced in the secondary coil due to Faraday’s law of electromagnetic induction. The equations of the transformer working principle PDF are given below

Then the induced emf in the second coil is given by,

𝑑∅

𝜀𝑠 = −𝑁𝑠 𝑑𝑡 − − − (1)

Also, the induced back emf in the primary coil is given by,

𝑑∅

𝜀𝑃 = −𝑁𝑃 𝑑𝑡 − − − (2)

Dividing equations (1) and (2,) we get   

𝜀𝑃=𝑁𝑠𝑁𝑃 (∵𝜀𝑠=𝑉𝑠 𝑎𝑛𝑑 𝜀𝑃=𝑉𝑃) 𝑉𝑠/𝑉𝑃=𝑁𝑠/𝑁𝑃−−−(3)

If there is no loss of energy while transforming, then there is no loss of energy, then

Input power = Output power

𝑃𝑖𝑛𝑝𝑢𝑡 = 𝑃𝑜𝑢𝑡𝑝𝑢𝑡

𝐼𝑃𝑉𝑃 = 𝐼𝑆𝑉𝑆

From (3) and (4),

𝑉𝑠

𝑉𝑃

𝐼𝑃 = 𝐼𝑆

− − − −(4)

𝑰𝑷 = 𝑽𝒔 = 𝑵𝒔 𝑰𝑺         𝑽𝑷         𝑵𝑷

The EMF equation helps to explain the relationship between the voltage, frequency, number of turns and magnetic flux in a transformer. The electromotive force (EMF) equation is:

$E=4.44fN\varphi$

where:

• $E$is the electromotive force (EMF) produced in volts
• $f$is the frequency of AC supply in hertz (Hz)
• $N$is the number of turns in the winding
• $\varphi$is the maximum flux in the core in webers (WB).

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There are mainly two types of transformers:

1. Step-up transformer
2. Step-down transformer

Step-up Transformer

We use a step-up transformer when a high voltage output is required. A step-up transformer converts low voltage to high voltage. We get high voltage when the number of turns in the secondary coil is more than the number of turns in the primary coil ( Np < NS ).

Step-down transformer:

A step-down transformer converts high voltage to low voltage. For this step up, the number of turns in the primary coil is more than the number of turns in the secondary coil (Np > NS).

Step-up Transformer

Step-down transformer

An ideal transformer is linear, lossless and perfectly coupled. Perfect coupling implies infinitely high core magnetic permeability and winding inductance and zero net magneto motive force (i.e. i_pn_p − i_sn_s = 0).

Transformer energy losses are dominated by winding and core losses. Transformers' efficiency tends to improve with increasing transformer capacity. The efficiency of typical distribution transformers is between about 98 and 99 per cent. In transformers, small energy losses do occur due to the following reasons

• Copper loss
• Eddy current loss
• Hysteresis loss
• Flux leakage
• Humming loss