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

Transformers are stationary electrical machines which transmit energy from systems with certain current and voltage values into systems with generally different current and voltage values but with identical frequency.
Two separate windings are on the same iron core.
Following connection to alternating voltage U_{1} there is a standstill current I_{0}. The magnetomotive force Q = I_{0} · N_{1} generates a magnetic alternating flow (F_{1}) in the iron core.
The input and output winding of an alternating voltage are induced in accordance with the induction law. A selfinduction voltage U_{10} arises in the input winding. It is counterpositioned in accordance with Lenz’s law on applied voltage. During idling operation  because of mutual induction  there arises the output voltage U_{20} which is simultaneously the terminal voltage U_{2}.
U_{1~} ® I_{0~} ® Q_{0~} ® F_{1~} ® U_{20~}
The value of the induced voltage is derived from the following equation:
_{}
_{} 
max. flow density 
A_{Fe} 
limb crosssection 
U_{0} 
induction voltage 
f 
frequency 
N 
number of turns 
The induction voltage increases along with the number of turns, the magnetic flow density in the iron core, the iron crosssection and the frequency.
Example:
Which maximum flow density occurs in an iron core of 16 cm^{2 }crosssection when a voltage of 380 V (50 Hz) is applied to the primary coil with 980 turns?
Given: A_{Fe} = 16 cm^{2}; N_{1} = 980; U_{1} = 380 V; f = 50 Hz
Sought: _{}
Solution:
_{}
_{}
_{}
_{}
_{} » 1.09 V · s · m^{2}
_{} » 1.09 T
The iron core evidences a maximum flow density of 1.09 T.