1. Lecture 2

2. Transformer
a transformer is a device that
1. transfers electrical power from one circuit to
another
2. it does so without a change of frequency
3. it accomplishes this by electromagnetic
induction and
4. where the two electric circuits are in mutual
inductive influence of each other.

4. 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.

6. The ideal transformer

9. 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.

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

11. 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

13. • 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.

14. 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
=BmA
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
mf
f
m 

Now rate of change of flux per turn means induced emf in volts.
So average emf turn =4fm volt
If flux  varies sinusoidally, then rms value of induced emf is obtained by
multiplying the average value with form factor.
1.11
valueaverage
valuerms
factorForm 
So rms value of emf/turn =1.11 4fm = 4.44fm volt

15. 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 )(44.4
2
2
1
1 iiimf
N
E
N
E

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
-
+