Faraday’s Law of
Electromagnetic Induction states that whenever there is a change in the flux
linking through a coil, an emf is developed in the coil. Thus for production of
emf, flux linking through the coil must change but for the flow of current
through the coil, the circuit must be complete i.e. coil should not be open for
the flow of current. For better understanding of Electromagnetic Theory one
must read “Principle of Electromagnetics by Matthew N.O. Sadiku.” This book is
just awesome and I guarantee that if one has gone through this book, his
concept of Electromagnetics will be crystal clear.

A Transformer works on this
basic principle of Faraday’s Law. Let us assume a Core Type Transformer as
shown in figure below.

As shown in the figure,
Primary winding of the Transformer is supplied with an alternating voltage
source V

_{1}while keeping the Secondary open. Due applied voltage V_{1}, an alternating current I_{e}starts flowing through N_{1}primary turns.
Thus alternating mmf of
Primary = N

_{1}I_{e}_{}

Because of this alternating
mmf, an alternating flux is set up in the core of Transformer which links with
the Primary as well as Secondary winding and as per Faraday’s Law of
Electromagnetic Induction, an emf E

_{1}& E_{2}are developed across the terminals of the Primary and Secondary winding.
This phenomenon is popularly
known as Transformer action.

Now, we will go further and
will have an insight of Two-winding Transformer. For the sake of clear
understanding, first of all we consider an Ideal Transformer. An Ideal
Transformer is one having the following characteristics:

- Negligible winding resistance.

- All the flux set up in the core links with the Secondary winding i.e. the flux is confined in the magnetic core of the Transformer.

- The core losses are negligible.

- Magnetization curve of core is linear.

Let the voltage V

_{1}applied to the Primary of Transformer be sinusoidal. Thus the current I_{e}will also be sinusoidal and hence the primary mmf N_{1}I_{e}must also be sinusoidal in nature. Note that flux Ø set up in the core of Transformer will be sinusoidal as the Primary mmf responsible for setting up the flux is sinusoidal.
Let,

Ø = Ø

_{m}Sinwt
Where Ø

_{m}is the maximum value of magnetic flux in Weber Wb and w = 2πf is the angular frequency in rad/sec.
Therefore,

Total flux linking through
the Primary = N

_{1}xØ
= N

_{1}Ø_{m}Sinwt
Hence,

Emf induced in the Primary e

_{1}= -d(N_{1}Ø ) / dt
= -N

_{1}wØ_{m}Coswt
= -N

_{1}wØ_{m}Sin(wt – π/2)
Thus we see that the emf e

_{1}induced in the Primary winding is sinusoidal and lagging behind the flux Ø by 90°.
Maximum value of induced emf
in Primary e

_{m}= N_{1}wØ_{m}_{}

So, e

_{m}= 2πfN_{1}Ø_{m}_{}

Now, the RMS value of
induced emf e in Primary winding E

_{1},
E

_{1}= 1.414xπfN_{1}Ø_{m}_{}

= 4.44fN

_{1}Ø_{m}……………………….(1)
It must be noted and
understand that the direction of emf induced the Primary winding will be in
such a direction to oppose the cause i.e. applied voltage here in this case. As
we have assumed the Transformer winding resistance negligible, so we can write
for Primary circuit,

V

_{1}= E_{1}…………………………(2)
Similarly, as the flux in
the Transformer core is Ø, this flux will also link with the Secondary to
induce an emf in the Secondary winding.

Flux linkage with the
Secondary winding = N

_{2}Ø
=N

_{2}Ø_{m}Sinwt
Hence,

Emf induced in the Secondary
e

_{2}= -d(N_{2}Ø_{m}Sinwt) / dt
= -N

_{2}wØ_{m}Coswt
= -N

_{2}wØ_{m}Sin(wt – π/2)
Maximum value of e

_{2}= N_{2}w
= 2πfN

_{2}Ø_{m}_{}

So,

RMS value of emf E

_{2}induced in the Secondary winding
= 4.44N

_{2}fØ_{m}……………….(3)
Thus we can write,

E

_{1}/ E_{2}= N_{1}/ N_{2}(From equation (1) & (3)) ………………(4)
E

_{1}/ N_{1}= E_{2}/ N_{2}= 4.44fØ_{m}_{}

Which means,

Emf per turn in Primary =
emf per turn in Secondary.

Consider the figure below.

As soon as switch S is
closed, a current I

_{2}starts flowing in the Secondary winding. The direction of this current will be in such a way to produce a magnetic flux opposite to the direction of working flux set up in the core. (This is as per the Lenze’s Law which says “Effect Opposes the Cause”). Thus the direction of current in the Secondary winding will be in anticlockwise direction; this is because current in anticlockwise direction will produce flux in upward direction in the core.
In this way we see that Secondary
current tends to oppose the working flux. Any reduction in working flux Ø will cause
a reduction in Primary emf E1 but as we have sen from from equation (2),

V

_{1}= E_{1}and V_{1}is constant.
This simply implies that
working flux in the core of Transformer must be constant. To have a constant
flux, Primary must draw an additional current I

_{1}’ from the source to compensate for the reduction caused by Secondary current.
Therefore, Compensating Primary
mmf = Secondary mmf

N

_{1}I_{1}’ = N_{2}I_{2}_{}

Any change in the Secondary
current is at once reflected by a corresponding automatic change in the Primary
current so that core flux remains constant.

Here I

_{1}’ is called load component of current.
Thus Primary current I

_{1}= I_{e}+I_{1}’
I

_{e}is called the Magnetizing current as this much of current is required to set up working flux in the core when the Secondary terminal is open.
Normally the value of magnetizing
current varies from 2-6% of full load current. If we neglect the magnetizing
current then,

N

_{1}I_{1}= N_{2}I_{2}_{}

N

_{1}/ N_{2}= I_{2}/ I_{1}_{}

Again as we have considered
Transformer winding have negligible resistance so for Secondary circuit,

E

_{2}= V_{2}_{}

Now, from equation (4),

E

_{1}/ E_{2}= V_{1}/ V_{2}= N_{1}/ N_{2}= I_{2}/ I_{1}_{}

For phasor diagram of
Transformer for No-Load and On-Load, read the previous post “Conceptual Phasor Drawing of Transformer.”

Note that, concept of
Transformer action is very important and one should know hoe to use and
implement this concept.

## No comments:

Post a Comment