single phase transformer

A static device used to transfer ac voltage from one circuit to other circuit through magnetic link without change in frequency.

working principle

When an alternating voltage (V1) is applied to the primary windings, an alternating flux (Φ) is set up in the core. This alternating flux links with both the windings and induces EMFs (E1 & E2) in them according to Faraday’s law of electromagnetic induction. E1 is named as primary EMF and E2 is named as secondary EMF.

E1 = – N1 d Φ /dt    &     E2 = – N2 d Φ / dt

Transformer does not change frequency of AC voltage / current because shape and magnitude of flux remains almost same on either side. Power of transformer (V1I1 = V2I2) remains same on either side. If voltage increases, then the current decreases maintaining the power constant.

transformer circuit

1)Electrical circuit which includes primary windings and secondary windings .The winding connected to AC source is called primary winding .The other connected to load is called secondary winding .The windings are made of copper to carry current.

2)Magnetic circuit includes magnetic core .Winding are wound on the core and are not electrically connected each other .The core is made of iron or silicon steel to carry flux .It is laminated to reduce the eddy current losses.

step-up transformer

Used to step up the voltage from low voltage level to high voltage level. It has more number of turns of coil on secondary side.

N2 > N1, V2 > V1, I2 < I1

step-down transformer

It is used to step down the voltage from high voltage level to low voltage level. It has less number of turns of coil on secondary side.

N2 < N1, V2 < V1 , I2 > I1

applications of transformer

1)Power transformers are used for transmission of electric power and usually used at power stations and grid stations.

2)Distribution Transformer are distributing electric power.

3)Auto Transformer are used to get variable voltage and also used as boosters in transformers.

4)Potential Transformers are used to step down voltages which are not measurable by voltmeter.

5)Current Transformers are used to step down line current which are not measurable by ammeter.

parts of transformer

There are following essential parts of transformer.


2)Magnetic / Iron Core

3)Transformer Tank

4)Terminals and Leads



7)Vent pipe

Limb :Vertical portion of the core on which wire is wounded

Yoke :Top and bottom horizontal portions of core that provides path for flux.

types of transformer

1)Core Type Transformer : Windings are wound on two legs of transformer core .Single magnetic circuit & windings encircle the core. Rectangle shape core with 2-limbs & 2-yokes

2)Shell Type Transformer : Both LV & HV windings placed at central limb. HV coil is between LV coils & LV coils are nearest to top & bottom of yoke. Double magnetic circuit with 3-limbs & 3-yokes. Shell shape core & sandwich windings are used. Used for low voltage purposes. Provides less cooling surface

turn ratio of a transformer

Ratio of primary number of turns N1 to secondary number of turns N2 , denoted by while we know that



As frequency and flux remain constant so replace them by constant “a” called turn ratio.

E1 / E2 = N1 / N2 = a

Where N1 / N2 is called turn ratio.

voltage transformation equation (k)

k is inverse of turn ratio so it is written as

k = 1 / a

k = N2 / N1

ideal transformer at no load

Ideal transformer is practically nothing but its study provides useful tool in the analysis of a practical transformer.


  1. Winding resistances (R1 & R2) = Zero
  2. Winding reactance (X1 & X2) = Zero
  3. Copper and core losses = Zero
  4. Leakage flux = Zero
  5. Zero voltage regulation = Zero
  6. Input = output
  7. Efficiency = 100 %

phasor diagram of ideal transformer

When an alternating voltage V1 is applied to the primary, it draws a small magnetizing current Im which lags behind the applied voltage by 90°. This alternating current Im produces an alternating flux Ф which is proportional to and in phase with it. The alternating flux links with both the windings and induces e.m.f. E1 in the primary and e.m.f. E2 in the secondary.

The primary e.m.f. E1 is, at every instant, equal to and in opposition to V1 (Lenz’s law). Both e.m.f E1 and E2 lag behind flux by 90°. Since flux f is common to both the windings, it has been taken as the reference phasor. Primary e.m.f. E1 and secondary e.m.f. E2 lag behind the flux f by 90°. Note that E1 and E2 are in phase. But E1 is equal to V1 and 180° out of phase with it.

practical transformer

Characteristics are given below

  1. Winding resistances (R1 & R2) ≠ Zero
  2. Winding reactance (X1 & X2) ≠ Zero
  3. Copper and core losses ≠ Zero
  4. Leakage flux ≠ Zero
  5. Zero voltage regulation ≠ Zero
  6. Input ≠ output
  7. Efficiency ≠ 100 %

phasor diagram of practical transformer at no load

No-load primary current I0 can be resolved into two rectangular components viz.

(i) The component IW in phase with the applied voltage V1. This is known as active or working or iron loss component and supplies the iron loss and a very small primary copper loss.

IW = I0 cos Ф0

(ii) The component Im lagging behind V1 by 90° and is known as magnetizing component. It is this component which produces the mutual flux Фo in the core.

Im = I0 sin Ф0

transformer losses

Transformer losses are appear on the form of heat in core and windings

 hysteresis losses

Associated with magnetization & demagnetization of the core during each half cycle of the flux.

eddy current losses

Induced emf in core sets up eddy current in core and hence eddy current losses occur.

leakage flux losses

Flux leaking from core to air produces self-inductance in coils which is loss.

copper losses

  1. Resistive heating losses in the primary and secondary windings of the transformer.
  2. Proportional to square of the current flowing in the windings.
  3. About 90 % of the total losses.
  4. Known as variable losses because they are different at different loads.

Why transformer power in KVA instead of KW?

1)Copper losses depend on current and iron losses depend on voltage and no other losses occur in transformer. Therefore total losses depend on Volt –Ampere (VA).

2)Losses do not depend on angle between volt and current. It means it is independent of power factor.

3)Electrical power on either side of transformer is constant (V1I1 = V2I2), so there is no need of power factor which is only required to compensate losses.


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