 Transformer (electrical engineering)

An electrical transformer transfers energy between electromagnetic coils through electromagnetic induction. A changing shared magnetic flux produces an electromotive force in each coil. In the ideal model, both coils link the same flux $\Phi (t)$; for $N_1$ and $N_2$ turns, Faraday's law of induction gives induced voltages proportional to $N_{1}d\Phi /dt$ and $N_{2}d\Phi /dt$. Their relative signs depend on the winding orientations.^[ref]

For sinusoidal operation, the ideal root mean square voltage magnitudes satisfyThe ideal lossless model also conserves transferred power. With negligible excitation electric current, its electric current magnitudes obey $I_1/I_2=N_2/N_1$. For a load electrical impedance $Z_L$, combining the voltage and electric current ratios gives the input electrical impedanceThus an electrical transformer changes the voltage-current relationship seen by a source as well as the voltage.^[ref]

For an ideal 10:1 turns ratio, a 230 V sinusoidal input produces 23 V at the secondary. A 23 ohm resistive load draws 1 A, corresponding to 0.1 A at the primary: both sides transfer 23 W. These are ideal-model calculations. Winding electrical resistance, magnetic hysteresis, eddy currents and incomplete shared flux introduce losses or departures from those ratios in a real electrical transformer. A constant flux produces no sustained induced secondary voltage.