= Transformer
{disambiguate=electrical engineering}
{wiki=Transformer}
= Electrical transformer
{synonym}
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 <electric potential differences>[voltages] proportional to $N_1\,d\Phi/dt$ and $N_2\,d\Phi/dt$. Their relative signs depend on the winding orientations.<Electromagnetic Fields and Energy by Hermann A. Haus and James R. Melcher>[Chapter 10, Faraday's law and volts per turn; section 10.1]{ref}
For sinusoidal operation, the ideal <root mean square> <electric potential difference>[voltage] magnitudes satisfy
$$
\frac{V_2}{V_1}=\frac{N_2}{N_1}.
$$
The 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 <electric potential difference>[voltage] and <electric current> ratios gives the input <electrical impedance>
$$
Z_{\rm in}=\left(\frac{N_1}{N_2}\right)^2Z_L.
$$
Thus an <electrical transformer> changes the voltage-current relationship seen by a source as well as the <electric potential difference>[voltage].<University Physics Volume 2 by Samuel J. Ling and others>[Section 15.6, equations 15.20–15.22; impedance formula derived here]{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 <electric potential difference>[voltage].
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