Lecture 2

Transformer

a transformer is a device that1. transfers electrical power from one circuit to

another2. it does so without a change of frequency3. it accomplishes this by electromagnetic

induction and4. where the two electric circuits are in mutual

inductive influence of each other.

Ideal Transformer

An ideal transformer is one which has no losses i.e. its winding have no ohmic resistance, there is no magnetic leakage and hence which has no I2R and core losses.

The ideal transformer

Induction law

The transformer is based on two principles: 1. an electric current can produce a magnetic field 2. a changing magnetic field within a coil of wire

induces a voltage across the ends of the coil (electromagnetic induction).

Changing the current in the primary coil changes the magnetic flux that is developed. The changing magnetic flux induces a voltage in the secondary coil.

Induction law

The voltage induced across the secondary coil may be calculated from Faraday's law of induction

same magnetic flux passes through both the primary and secondary coils in an ideal transformer, the instantaneous voltage across the primary winding equals

Taking the ratio of two equations

• The changing magnetic field induces an emf across each winding.

• The primary emf, acting as it does in opposition to the primary voltage, is sometimes termed the counter emf.This is in accordance with Lenz's law, which states that induction of emf always opposes development of any such change in magnetic field.

EMF Equation of a Transformer

Let, N1 = No. of turns in primary

N2 = No of turns in secondary

m = maximum flux in core in webers

=BmA

f = frequency of AC input in Hz

As shown in Fig. 32.14, flux increases from its zero value to maximum value m in one quarter of the cycle i.e. in (1/4f) second .So average rate of change of flux= voltorwb/s4

4/1 mffm

Now rate of change of flux per turn means induced emf in volts.

So average emf turn =4fm volt

If flux varies sinusoidally, then rms value of induced emf is obtained by multiplying the average value with form factor.

1.11 valueaverage

valuermsfactorForm

So rms value of emf/turn =1.11 4fm = 4.44fm volt

Now rms value of the induced emf in the whole of primary winding

= (induced emf/turn)(No. of primary turns)

)(144.4144.41 iAmBfNmfNE Similarly, rms value of the induced emf in the secondary is,

)(244.4244.42 iiAmBfNmfNE

It is seen from (i) and (ii) that )(44.422

11 iiimfN

ENE

It means that emf turns is the same in both the primary and secondary windings.

In an ideal transformer on no load V1=E1 and V2=E2, where V2 is the secondary terminal voltage.

V1

-

+ + E2 -

+ E1 -

V2

-

+