# Efficiency, Induced EMF, Power, and Loss of Transformer

When some voltage is induced in the primary of a transformer, a magnetic flux created in the primary is produced in the secondary due to mutual induction, which generates some voltage in the secondary. The strength of this magnetic field is created when the current increases from zero to the maximum value which is given by dφ/dt.

The magnetic lines of flux pass through the secondary winding. The number of turns in the secondary winding determines the induced voltage. Thus the amount of induced voltage due to which will be determined

where N = number of turns in the secondary winding,

The frequency of this generated voltage will be the same as the frequency of the primary voltage. The peak amplitude of the output voltage will be affected if the magnetic loss is high.

## The efficiency of a transformer

The amount or intensity of power loss in a transformer determines the efficiency of the transformer. Efficiency can be understood in terms of the power loss between the primary and secondary of the transformer.

Therefore, the ratio of the power output of the secondary winding to the power input of the primary winding can be termed the efficiency of the transformer. it can be written as:

Efficiency is usually denoted by. The above equation is valid for an ideal transformer where there will be no loss and the entire energy in the input is transferred to the output.

Therefore, if losses are to be considered and if efficiency is to be calculated under practical conditions, the equation given below should be considered.

Otherwise, it can also be written as,

It should be noted that input, output, and loss are all expressed in terms of power, i.e. in Watts.

### Induced EMF

Now consider that both the primary and secondary coils have a single turn each. If one volt is applied without damage to one turn of the primary, then in the ideal case the current flows, and the magnetic field is produced to induce the same volt in the secondary. Hence the voltage on both sides is the same.

But the magnetic flux varies sinusoidally which means,

Then the basic relation between the induced emf and the coil winding of n turns is,

Where,

• f = flux frequency in hertz = ω/2π.
• N = number of coil windings.
• ∅ = flux density in webers.

This is known as the transformer emf equation.

Since the alternating flux produces a current in the secondary coil, and this alternating flux is produced by the alternating voltage, we can say that only an alternating current AC can help the transformer to work. Hence a transformer does not operate on DC.

#### Power of a Transformer

When an ideal transformer is assumed to be without losses, the power of the transformer will remain constant, because product I, when the voltage V is multiplied by the current, is constant.

We can say that the power in the primary is equal to the power in the secondary as the transformer takes care of that. If the transformer steps up the voltage or increases the voltage, the current is reduced and if the voltage is stepped down, the current is increased to keep the output power constant.

Hence the primary power is equal to the secondary power.

Where P = Primary phase angle and S = Secondary phase angle.

Related Tutorial: Types of Transformers.

#### Loss in Transformer

In practical applications, any device has some disadvantages. The main losses that occur in a transformer are copper loss, core loss, and flux leakage.

##### Copper Losses

The loss of copper is the loss of energy, which is caused by the heat generated by the current flowing through the windings of the transformer. These are also called “I2R losses” or “I squared R losses” because the energy lost per second increases with the square of the current through the winding and is proportional to the electrical resistance of the winding.

It can be written in an equation as:

Where,

• IP = Primary Current.
• RP = Primary Resistance.
• IS = Secondary Current.
• RS = Secondary Resistance.
##### Core Losses

Core loss is also called iron loss. These disadvantages depend on the main material used. They are of two types, hysteresis and eddy current loss.

• Hysteresis Loss − The induced AC fluctuates and falls as the magnetic flux reverses direction according to the induced AC voltage. These random fluctuations cause some energy loss in the core. Such loss can be called hysteresis loss.
• Eddy Current Loss − Some current is induced in the core which is continuously circulated. These currents produce some loss which is called eddy current loss. Actually, the varying magnetic field is known to induce current only in the secondary winding. But it also induces a voltage in nearby conducting material, resulting in loss of energy.
• Flux Leakage − Although the flux linkages are strong enough to produce the required voltage, there will be some flux that leaks out in practical applications and results in loss of energy. Though it is low, when it comes to high energy applications this disadvantage can also be counted.