Transformer

The transformer is a device used to convert low alternating voltage at high current into the high alternating voltage at low current and vice versa. The transformer is an electrical device used to increase or decrease alternating voltage.

Types of transformers

There are two types of transformers. They are:

1. Step-up transformer:

   The transformer which converts low a.c. the voltage at high current into high a.c. the voltage at low current is called the step-up transformer.

2. Step-down transformer:

   The transformer which converts high a.c. the voltage at low current into a low a.c. the voltage at high current is called the step-down transformer.

Principle:

It is based on the principle of mutual induction i.e. when the magnetic flux linked with a coil is changed, e.m.f. is induced in the nearby coil.

Construction

It consists of two windings or coils, the primary and secondary, wound on common laminated soft-iron core. The coil connected to the a.c. the source is called primary coil and the coil connected to the load is called secondary coil. The primary coil along with load is called primary circuit and the secondary coil along with load is called secondary circuit.

Theory

When an a.c. source of e.m.f E_p is connected to the primary coil, an alternating current flows through it so that alternating magnetic field is produced and hence magnetic flux linked with the coil and N_s be the number of turns in the primary and secondary coils respectively. The iron coil is capable of coupling all of the magnetic flux \(\phi \) produced by the turns of the primary coil with the secondary coil.

\begin{align*} \epsilon_p &= -N_p\frac {d\phi }{dt} \dots (i) \\ \text {The induced e.m.f. in the secondary coil,} \\ \epsilon_s &= N_s \frac {d\phi }{dt} \dots (ii)\\ \text {Dividing equation}\: (ii)\:\text {by}\:(i), \: \text {we get}\\ \frac {\epsilon _s}{\epsilon _p} &= \frac {N_s}{N_p} \\ \end{align*}

\begin{align*} \text {where}\: \frac {N_s}{N_p} &= \sqrt {\frac {L_P}{L_S}} = k \: \text {transformation ratio.} \\ \text {Here,}\\ L_P &= \text {coefficient of self induction of primary coil} \\ L_S &= \text {coefficient of self induction of secondary coil} \\ \therefore {\epsilon _s}{\epsilon _p} &= \frac {N_s}{N_p} = K \dots (iii) \\\end{align*}

\begin{align*} \text {For step-down transformer,} \: K< 1\\ \text {For step-up transformer} \: K >1 \\ \text {For an ideal transformer} \\ \text {Output power} &= \text {Input power} \\ \text {or,} \: {\epsilon _s}{\epsilon _p} &= \frac {I_p}{I_s} \dots (iv) \\ \text {In general,}\: \epsilon \propto \frac 1I \\ \end{align*}

A step-up transformer increases the alternating voltage by decreasing the alternating current and a step-down transformer decreases the alternating voltage by increasing the alternating current.

For a transformer,

\begin{align*}\text {efficiency,}\: \eta &= \frac {\text {output power}}{\text {input power}} = \frac {E_SI_S}{E_PE_P} \\ \end{align*}

Energy Losses in a transformer

1. Copper Losses
   Energy lost in windings of the transformer is known as copper loss. When current flows through copper wires, there is loss in power. This can be reduced by using thick wires for windings.
2. Flux losses
   In the actual transformer, the coupling between primary and secondary coil is not perfect. So certain amount of electrical energy supplied to the primary coil is wasted.
3. Iron losses
   a)Eddy current losses:
   When a changing magnetic flux links with the iron core of the transformer, eddy currents are set-up. These eddy currents in the iron core produce heat which leads to wastage of energy. This can be reduced by using laminated core.
   b. Hysteresis losses
   When alternating current passes through the primary coil of the transformer, the iron core of the transformer is magnetized and demagnetized over a complete cycle. Some energy is lost during magnetizing and demagnetizing the iron core. The energy loss in a complete cycle is equal to the area of the hysteresis loop. This can be minimized by using the suitable material having narrow hysteresis loop for the core of a transformer.
4. Losses due to vibration of core
   A transformer produces humming noise due to magnetostriction effect. Some electrical energy is lost in the form of mechanical energy to produce vibration in the core.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.