A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors — the transformer's coils or "windings". Except for air-core transformers, the conductors are commonly wound around a single iron-rich core, or around separate but magnetically-coupled cores. A varying current in the first or "primary" winding creates a varying magnetic field in the core (or cores) of the transformer. This varying magnetic field induces a varying electromotive force (EMF) or "voltage" in the "secondary" winding. This effect is called mutual induction.

If a load is connected to the secondary, an electric current will flow in the secondary winding and electrical energy will flow from the primary circuit through the transformer to the load. In an ideal transformer, the induced voltage in the secondary winding (V_S) is in proportion to the primary voltage (V_P), and is given by the ratio of the number of turns in the secondary to the number of turns in the primary as follows:

\frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}}

By appropriate selection of the ratio of turns, a transformer thus allows an alternating current (AC) voltage to be "stepped up" by making N_S greater than N_P, or "stepped down" by making N_S less than N_P.

Transformers come in a range of sizes from a thumbnail-sized coupling transformer hidden inside a stage microphone to huge units weighing hundreds of tons used to interconnect portions of national power grids. All operate with the same basic principles, although the range of designs is wide. While new technologies have eliminated the need for transformers in some electronic circuits, transformers are still found in nearly all electronic devices designed for household ("mains") voltage. Transformers are essential for high voltage power transmission, which makes long distance transmission economically practical.

First steps: experiments with induction coils

What would become the "transformer principle" was revealed in 1831 by Michael Faraday in his demonstration of electromagnetic induction, but without recognition of its future role in manipulating EMF. The first "induction coils" to see wide use were invented by Rev. Nicholas Callan of Maynooth College, Ireland in 1836, one of the first researchers to realize that the more turns the secondary winding has in relation to the primary winding, the larger the increase in EMF. Induction coils evolved from scientists' and inventors' efforts to get higher voltages from batteries. Rather than alternating current (AC), their action relied upon a vibrating "make-and-break" mechanism that regularly interrupted the flow of direct current (DC) from the batteries. Between the 1830s and the 1870s, efforts to build better induction coils, mostly by trial and error, slowly revealed the basic principles of transformers. Efficient, practical designs did not appear until the 1880s, but within a decade the "transformer" would be instrumental in the "War of Currents", and in seeing AC distribution systems triumph over their DC counterparts, a position in which they have remained dominant ever since.