e greater. For example, suppose a power of 50 watts is supplied to a resistive load from a transformer with a turns ratio of 25:2.
- P = E·I (power = electromotive force · current)
50 W = 2 V · 25 A in the primary circuit
- Now with transformer change:
50 W = 25 V · 2 A in the secondary circuit.
The high-current, low-voltage windings have fewer turns of (usually) thicker wire. The high-voltage, low-current windings have more turns of (usually) thinner wire.
The electromotive force (EMF) developed in the secondary is proportional to the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. Neglecting all leakage flux, an ideal transformer follows the equation:
Where is the voltage in the primary coil, is the voltage in the secondary coil, is the number of turns of wire on the primary coil, and is the number of turns of wire on the secondary coil. This leads to the most common use of the transformer: to convert power at one voltage to power at a different voltage.
Neglecting leakage flux, the relationship between voltage, number of turns, magnetic flux intensity and core area is given by the universal emf equation:
Where is the sinusoidal root mean square (RMS) voltage of the winding, is the frequency in hertz, is the number of turns of wire, is the area of the core (square units) and is magnetic flux density in webers per square unit. The value 4.44 collects a number of constants required by the system of units.
In normal operation, a transformer winding should never be energised from a constant DC voltage source, as this would cause a large direct current to flow. In such a situation, in an ideal transformer with an open circuit secondary, the current would rise indefinitely as a linear function of time. In practice, the series resistance of the winding limits the amount of current that can flow, until the transformer either reaches thermal equilibrium or is destroyed. DC is occasionally applied to large power transformers in order to "bake out" water prior to adding the cooling oil and commencing normal operation.
Those credited with the invention of the transformer include:
- Michael Faraday, who invented an 'induction ring' on August 29, 1831. This was the first transformer, although Faraday used it only to demonstrate the principle of electromagnetic induction and did not foresee the use to which it would eventually be put.
- Lucien Gaulard and John Dixon Gibbs, who first exhibited a device called a 'secondary generator' in London in 1881 and then sold the idea to American company Westinghouse. This may have been the first practical power transformer, but was not the first transformer of any kind. They also exhibited the invention in Turin in 1884, where it was adopted for an electric lighting system. Their early devices used a linear iron core, which was later abandoned in favour of a more efficient circular core.
- William Stanley, an engineer for Westinghouse, who built the first practical device in 1885 after George Westinghouse bought Gaulard and Gibbs' patents. The core was made from interlocking E-shaped iron plates. This design was first used commercially in 1886.
- Hungarian engineers Ottó Bláthy, Miksa Déri and Károly Zipernowsky at the Ganz company in Budapest in 1885, who created the efficient "ZBD" model based on the design by Gaulard and Gibbs.
- Nikola Tesla in 1891 invented the Tesla coil, which is a high-voltage, air-core, dual-tuned resonant transformer for generating very high voltages at high frequency.
Transformers come in a range of sizes from a thumbnail-sized coupling transformer hidden inside a stage microphone to gigawatt units used to interconnect large portions of national power grids, all operating with the same basic principles and with many similarities in their parts.
- Up to 1 watt: Signal transformers, interstage coupling
- 1 - 1000 watts: Small power transformers, filament transformers, audio output transformers
- 1 kilowatt - 1 megawatt: Power transformers; larger units in this range may be oil filled
- 1 megawatt and over: Large power trans