Transformer

A transformer is a static electrical device used to transfer electrical power from one circuit to another keeping the supply frequency constant. We can increase or decrease the voltage in the secondary of the transformer with the corresponding changes in current and hence the power transfer will be almost constant if we neglect the losses. This transfer of power and change in secondary voltage will take place due to linkage of common magnetic flux and mutual induction between the two coils as explained below in working principle of transformer.

Working Principle: A transformer works on the principle of Faraday’s laws of electro magnetic induction, which states that “whenever a closed circuit coil is placed in an alternating magnetic field, an electro motive force (e.m.f.) will induced in that coil and magnitude of this induced e.m.f. will depends upon the number of turns in the coil.” To understand the working principle

When the primary winding of the transformer is connected to a.c. supply, the magnetic flux (F) will be set up and circulate in the laminated magnetic core. This magnetic flux will be alternating in nature as the supply frequency and links with both the windings (Primary and secondary) of the transformer. Now according to faraday’s laws of electromagnetic induction an e.m.f. will be induced in the secondary winding due to mutual induction. This induced e = n dF/dt in the secondary winding will depend upon the rate of change of flux and number of turns. If the number of turns in the secondary winding is greater than primary, the transformer will act as step up transformer and vice-versa. Whether a transformer is step up or step down depends upon the transformation ratio (K), which is explained below.

Transformation Ratio (K): As discussed above, when the primary winding of the transformer is connected across the a.c. supply, an alternating current will flow in the primary winding. And as a result of this alternating current, an alternating magnetic field (F) will be set up and circulate in the laminated core

This circulating alternating magnetic flux will link with both the primary and secondary windings of the transformer and as a result of it; an alternating electromotive force(e.m.f.) will be induced in these windings, due to self and mutual induction respectively. Induced e.m.f. (E 1 ) in the primary winding will be almost equal and opposes the applied voltage and hence known as back e.m.f. This induced e.m.f. (E 2 ) in the secondary winding depends upon the rate of change of flux and number of turns

(e = n dF/dt).

Let N 1----> Number of turns in the primary winding.

N 2----> Number of turns in the secondary winding.

E 1 --->Induced e.m.f. in the primary winding.

E 2 --->Induced e.m.f. in the secondary winding.

V 1--->In put a.c. voltage to the primary winding.

V 2---> Out put a.c. voltage across the load.

Induced voltage in the primary wi nding per turn =(E 1/N 1)volts

Since the same flux will link with both the primary and secondary windings.

So, this induced e.m.f. in the secondary winding will be

Where K is called the transformation ratio.

If K is greater than 1, the transformer is step-up transformer and

If K is less than 1, the transformer is step-down transformer.

For an ideal transformer input power = out put power

Or V 1 I 1 = V 2 I 2

(V 2/ V 1)= (I 2/I 1)=  K

Where K is known as transformation ratio of the transformer.