Question

Describe the principle, construction and working of a transformer. What are the energy losses in it?

Answer 1

Transformer: A transformer is a device for converting a large alternating current at low voltage into a small alternating current at high voltage and vice-versa.

If the voltage is stepped up and the current is decreased, the transformer is called step up transformer and if the voltage is lowered and the current is increased, the transformer is called step down transformer.

Principle: It is based upon the principle of mutual inductance i.e. whenever magnetic flux linked with a coil is changed, an induced e.m.f. is produced in the neighbouring coil.

Construction: A transformer consists of two coils of insulated wire containing different number of turns wound separately on a continuous soft iron core as shown in Fig. The coil to which the electric energy is fed is called the primary, whereas the coil from which the energy is drawn is called the secondary. The two coils of wire are close to each other but are not electrically connected. The entire magnetic flux coming out of one will practically remain in the iron core, and hence pass through the other coil. The soft iron core provides a good path for the magnetic lines of force and therefore, helps in making almost all of them pass through the secondary coil.

Action. Alternating current is fed to the primary. The alternating current in the primary produces an alternating magnetic flux in the core which passes through the secondary coil. Since magnetic flux remains practically confined within the core, the magnetic flux linked with the secondary is almost the same as that passing through the primary. The changing magnetic flux produces an induced e.m.f. in the secondary and also gives rise to self-induced (back) e.m.f. in the primary.

Consider the terminals of secondary coil to be open. Let Np and N_s be the number of turns in the primary and secondary coils respectively. Let Φ be the magnetic flux linked with the primary and the secondary at any instant. The induced e.m.f. in primary and secondary coils are given by:

E_p = -N_p \(\frac{d\phi}{dt}\)

and E_s = -N_s \(\frac{d\phi}{dt}\)

Thus \(\frac{E_s}{E_p} = \frac{N_s}{N_p}\) ...........(i)

The ratio of the number of turns in the secondary to that in the primary is called transformation ratio.

If a step up transformer, N_s > N_p, i.e. the transformation ratio is greater than 1 so that E_s > E_p.

In step down transformer, N_s < N_p i.e., transformation ratio is less than 1. so that E_s < E_p.

Output current: Further, according to the law of conservation of energy whether device is possible which can give any net gain of energy. Therefore, assuming no energy losses in the transformer, the energy drawn from the secondary is equal to that fed into the primary. Or, in other words,

Power output = Power input

If Ip and Is are the values of the currents in the primary and the secondary coils respectively, we have

I_s E_s = I_p E_p

or \(\frac{E_s}{E_p} = \frac{I_p}{I_s}\)

Thus as the voltage in the secondary increases, the current proportionately falls and vice versa i.e., whatever we gain in voltage, we stand to lose that much in current.

The efficiency of transformer is defined as

η = \(\frac{\text {Output power} }{\text {Input power}}\)

In an actual transformer, due to eddy currents in the core and also magnetic hysteresis of the core, part of the energy is actually lost.

Losses: Transformer is one of the most efficient machines known and its efficiency is high as 90-99%. It suffers from the following main losses

1. Copper loss: Energy lost as heat produced in copper wire used in the winding when current is passed through them (given by I₂R). This loss is minimized by using thick wire as their resistance is low.
2. Iron loss: Energy lost due to eddy currents formed in the core. This can be eliminated by using laminated iron core.
3. Hysteresis loss: It is the energy lost as work done in carrying the iron core through cycles of magnetization and demagnetization. This can be minimised by selecting iron with special magnetic properties to be used as core.
4. Magnetic flux leakage: Due to imperfect insulation, some of the magnetic flux leaks and causes an energy loss.
5. Humming loss: Due to passage of a.c. the core starts vibrating and produces humming sound. This sound production is called humming loss.

Uses

• Transformer is used in T.V., tape recorders, computers, air conditioners etc.
• In induction furnace.
• Step down transformer is used for welding purpose.
• Transformer is used for transmission of a.c. over long distances.