### An ideal transformer and a practical transformer.

Transformer: It is an electrical machine that transfers electrical energy from one circuit to another circuit without an electrical connection.

Transformers have two or more coils depending on the requirement. One coil is connected to the source and the other coils are connected to loads(depending on the connection).

We will mainly talk about two coil transformer.

### Ideal Transformer

A ideal transformer has following properties:

• The internal resistance of the primary and secondary coil is zero
• There is no leakage flux and therefore no leakage reactance. All the fluxes are confined to the ferromagnetic core of the transformer.
• There is negligible core loss, ohmic loss (The core loss consists of hysteresis loss and the eddy current loss).
• Since there are no losses therefore temperature rise in the transformer is negligible.
• The permeability of the ferromagnetic core is infinite. And therefore exciting current required to establish flux in the core is negligible.
• Because there are no losses, no leakage fluxes, therefore the efficiency of the ideal transformer is 100%.

But we in the real-life do not encounter ideal machines, the property of a real transformer, therefore, has deviation.

### Practical Transformer

• Every material opposes the flow of the current to some extent. Similarly, the primary and the secondary coil also oppose the flow of the current i.e. the coils have some internal resistance.

The resistance of the coil is given by:

R=ρ*l/A

ρ= resistivity of the wire

l= length of the wire

A= cross section of the wire

• Actually, there is leakage flux. The leakage fluxes are established across the coil. Because the flux cannot be confined to the core only.
• There is core loss and ohmic loss in the practical transformer.

#### Hysteresis Loss

If the voltage supplied is v=v(max)*sin(ωt) then for the positive half of the cycle energy flows from the source to the coil. This energy magnetizes the core. But for the negative half cycle energy return from the coil to the source.

But the energy that returns back is actually less than the energy which flows from the source to the coil. The remaining energy dissipates in the form of heat.

#### Eddy-current Loss

Since the voltage supply is varying with tim²²e so the flux establishes in the core will also vary with time.

This varying flux in turn will produce a current in the surface of the ferromagnetic core. This current is called Eddy current. This also gives rise to i²r loss in form of heat.

#### Ohmic Loss

The internal resistance of the coils will rise to i²r loss.

In this case, i=current flowing in the primary coil, r= internal resistance of the coil.

And in the previous case i=eddy current loss, r=internal resistance of the core.

• The losses produce heat and it will give rise to the temperature. But the temperature rises to only a certain value. And this value differs for different transformers.
• There is a certain value of permeability for every material. And it is very high for ferromagnetic material, therefore ferromagnetic material is used as a core of the transformer.
• And as no machine is 100% efficient therefore the efficiency of the transformer is also not equal to 100%. But the transformer is the most efficient electrical machine as no mechanical action is involved in it.