# Concept of Transformer Action

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.

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}Sinωt

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}Sinωt

Hence,

Emf induced in the Primary e_{1}= -d(N_{1}Ø ) / dt

= -N_{1}ωØ_{m}Cosωt

= -N_{1}ωØ_{m}Sin(ωt – 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}ωØ_{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}Sinωt

Hence,

Emf induced in the Secondary e_{2} = -d(N_{2}Ø_{m}Sinωt) / dt

= -N_{2}ωØ_{m}Cosωt

= -N_{2}ωØ_{m}Sin(ωt – π/2)

Maximum value of e_{2}= N_{2}ωØ_{m}

= 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}

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