Electrical Machines  Basic vocational knowledge (Institut für Berufliche Entwicklung, 144 p.) 
8. Transformer 
8.1. Transformer principle 

A few field lines already close before reaching the output coil (Figure 125) so that flow F_{1} can be divided into a maximum flow F_{K} which saturates both coils and a leakage flow F_{S}.
The leakage flow may be ignored in regard to the unloaded transformer (idling). Therefore the following applies:
_{}
According to the transformer equation
_{}and
_{}.
If we relate both equation then
_{}
Shortening gives us
_{}
During idling no current flows into the output winding, thus there is no voltage decrease. Consequently the induced voltage U_{20} equal to the terminal voltage U_{2} (Cp Figure 125):
Figure 125  Transformer principle
1 Input winding/upper voltage winding/primary winding, 2 Output winding/under voltage winding/secondary winding
U_{20} = U_{2}
In the event of minimal idling current I voltage decrease in the input winding is negligibly minimal. We therefore have
U_{10} = U_{1}which results in
_{}
The voltages behave like the numbers of turns.
The interrelationship of the numbers of turns is known as the transformation ratio We have:
_{}
The rated voltages U_{1n} and U_{2n} are indicated on the rating plate of the transformer.
Example:
What secondary terminal voltage arises in a transformer where 380 V is applied to the primary winding of 980 turns and the secondary winding has 594 turns?
Given: U_{1} = 380 V; N_{1} = 980; N_{2} = 594
Sought: U_{2}
Solution:
_{}
_{}
_{}U_{2} » 230 V