Definition – Electrical transformer is a static device which transforms electrical energy from one circuit to another with the help of mutual induction between two windings with no direct electrical connection. It transforms power from one circuit to anotherwithout changing its frequency. It transforms high voltage in one circuit to low voltage in another circuit & vice versa.

Transformer – Working Principle

It works on the principle of operation of mutual inductance between two circuits which are linked by a common magnetic flux. A basic transformer consists of two coils that are electrically separate but are magnetically linked through a core (linked mechanically). The working principle of the transformer can be understood from the figure below.

A transformer has primary and secondary coils (or windings). These two coils are mounted on a laminated core (in strip form). When AC supply is applied to first coil (or primary winding), an alternating flux is produced in the core,when this flux is linked with secondary coil, an emf (electro motive force) is induced in secondary coil (or secondary winding).

This can be explained with the help of Faraday’s laws of Electromagnetic Induction

Average Emf,Eav=N dØ/dt

(Where N = number of turns of coil&dØ/dt  = rate of change of flux).

If the second coil circuit is closed (when load is connected), a current flows in it.Therefore, we can see that secondary voltage can be increased & decreased at suitable level as induced emf is directly proportional to number of turns of coil.

EMF Equation of Transformer

We have seen that average emf ,Eav = N dØ/dt,

Therefore, RMS value of Emf, Erms= 1.11 N dØ/dt(where Eav= 1.11Erms)

Or                                                Erms= 1.11 N (4fØmax)

Where, max value of dØ/dt =Ømax/(1/4)f= 4fØmax

So, Erms = E =  4.44 N f Ømax

Now, let us apply this equation for both primary & secondary windings –

Induced emf in primary winding –  1= 4.44f N1Ømax

Similarly, Induced emf in secondary winding –  2= 4.44f N2Ømax

(Note- in both equations, value of max flux, Ømaxis same as both windings are linked with same flux).

In an ideal transformer on no load, applied voltage, V1 is equal to induced emf, 1 in primary winding & terminal voltage V2 is equal to induced emf, 2 in secondary winding.

Hence, we can say V1 = 1    and V2 = 2

Where – Ømax  = Maximum flux in the core in webers (Wb), f   = Frequency of flux  in hertz (HZ)

N1=  Number of turns in primary,            N2= Number of turns in secondary

(Note– The frequency of induced emf is the same as that of the flux or that of supply voltage. It means frequency doesn’t change during the process of energy transformation).

Voltage Transformation Ratio (K)

It is the ratio of secondary voltage to the primary voltage. It is designated by letter K. Hence from the above equations we get

K =  V2/ V1 =  E2/ E1 = N2/N1

For step up transformer     —    N2>N1  or K>1 ,

For step down transformer     —    N2<n1  or K<1   ,</n

Current Ratio –

In an ideal transformer, the losses are negligible, therefore – output = input

orV2I2 = V1I1  or E2I2 = E1I1

Or, I2/I1 = E1/E2 = N1/N2 = 1/K

Hence, primary & secondary currents are inversely proportional to their turns respectively. Or we can say that when secondary voltage increases, the current in secondary winding decreases & vice versa.

(Note-A transformer doesn’t work on DC supply& if we will try, primary winding will be burnt due heavy current drawn from incoming supply. The reason is clear that when dc supply is applied to a transformer, the flux produced will not vary & remain constant, so no emf will be induced in the secondary winding. Also no back emf will be induced in the primary winding. This situation is a short circuit case for primary winding.)


Transformers can be classified on the basis of types of construction, types of cooling etc.
a) On the basis of construction

Transformers can be classified into two types –  (i) Core type transformer and (ii) Shell type transformer, which are described below.

(i) Core type transformer

In core type transformer, windings are cylindrical in shape & mounted on the core limbs as shown in the left figure above. Both the windings are divided & half of each winding is placed on each limb. The cylindrical coils have different layers and each layer is insulated from each other. Materials like paper, cloth or mica can be used for insulation. Low voltage windings are placed nearer to the core, as they are easier to insulate.

(ii) Shell type transformer

The coils are former wound and mounted in central core or we can say that iron core surrounds windings. The entire flux passes through the central core & is divided outside into two parts.Sandwich type winding is used in which primary windings are sandwiched by secondary windings.

(b) On the basis of their purpose –

  1. As a Step up transformer: to increase output/secondary voltage for transmission purpose.
  2. As a Step down transformer: to decrease secondary voltage for distribution purpose.

(c) On the basis of type of supply

  1. Single phase transformer
  2. Three phase transformer

(d) On the basis of their use

  1. Power transformer: for high voltage transmission purpose.
  2. Distribution transformer: for distribution purpose, generally at lower voltage.
  3. Instrument transformer: For metering & protection purpose such asCurrent transformer (CT)&Potential transformer (PT)

(e)On the basis of cooling methods

  1. Oil immersed natural air cooled type,
  2. Oil immersed forced air cooled type,
  3. Oil immersed Water cooled type,
  4. Oil immersed Forced oil cooled type,
  5. Air blast type.

Transformer losses & efficiency

An electrical transformer is a static device, hence there is no friction and windage losses (known as mechanical losses). A transformer only consists of electrical losses -1)ironlosses and, 2) copper losses.

Efficiency of Transformer

In ideal case – Efficiency —–      Output = Input = 100%

But, practically,   Efficiency = Output/Input  or

= (Input – Losses) / Input  or

= 1 – (Losses/Input )

Transformers are the most highly efficient electrical devices. Most of the transformers have efficiency between 95% to 98.5% on full load.

Losses in transformers– Normally there are two types of losses occur in transformers –

1) Core or iron losses, 2) Copper losses

1)Core losses or Iron losses –

The losses which occur due to magnetic propertiesof the material (caused by alternatingflux) used for construction of core are called core losses or iron losses.Eddy current loss and hysteresis loss are examples of core losses.

Eddy current loss in transformer: In transformer, due to these eddy currents, some energy is dissipated in the form of heat.

When AC current is supplied to the primary winding which sets up alternating magnetizing flux. Major portion of this flux links with secondary winding &emf is produced in it. But some part of this flux also gets linked with other conducting parts like steel core or iron body or the transformer, which will result in induced emf in those parts, causing small circulating current in them. Eddy current losses depend on square of – a) Max flux density, b) Supply frequency & c) Lamination thickness.

Hysteresis loss in transformer: Hysteresis loss occurs due to alternating flux in the core. Its value depends onthe volume and grade of the iron, frequency of magnetic reversals and value of flux density. Hysteresis losses occurring per seconds are given below by Steinmetz formula:                                       Wh= ηBmax1.6fV (watts)

where,   η = Steinmetz hysteresis constant,              V = volume of the core in m3

Bmax = Value of flux density,f  = frequency of magnetic reversal

NoteIron losses remain constant from no load to full load because both eddy current & hysteresis losses depend upon the maximum flux density & its frequency in the core of the transformer.

2) Copper loss in transformer –

Copper loss is due to resistance of the transformer windings.  Copper loss for the primary winding is I12R1 and for secondary winding is I22R2.

Where, I1 and I2 are current in primary and secondary winding respectively,

R1 and R2 are the resistances of primary and secondary winding respectively. It is clear that Cu loss is proportional to square of the current, and current depends on the load. Hence,copper loss in transformer varies with the load, more load causes more Cu loss.

Note– Efficiency of a transformer will be maximum when copper loss and iron losses are equal i.e                 —           Copper loss = Iron loss.



As we have seen above, ordinary or commercial efficiency of a transformer can be given as-Ordinary or Commercial Efficiency = Output (in watts) / Input (in watts).

But performance of some types of Transformer can’t be judged by this efficiency. For example, distribution transformers have their primaries energized all the time. But, their secondary supply has little load or less load during day time &heavy during evening till midnight.

So, we can say that during day time transformer is having considerable Core Losses & copper losses are negligible while in the evening, Copper losses are considerably high as transformers are loaded in the evening. Therefore,the performance of such transformers is compared on the basis of energy consumed in one day.

All DayEfficiency = Output (in watts) / Input (in watts) ……(in 24 Hrs)

(Note – All day efficiency of a transformer is always less than ordinary efficiency of it.)