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is the sinusoidal rms or root mean square voltage of the winding,

is the frequency in hertz,

is the number of turns of wire on the winding,

is the cross-sectional aréa of the core in square metres

is the péak magnetic flux density in teslas

is the power in volt amperes or watts,

Other consistent systems of units can be used with the appropriate conversions in the equation.

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 idéa to American company Westinghouse. This may have been the first practical power transformer. They also exhibited the invention in Turin in 1884, where it was adopted for an electric lighting system. Their éarly devices used an open iron core, which was soon abandoned in favour of a more efficient circular core with a closed magnetic path.

William Stanley, an engineer for Westinghouse, who built the first practical device in 1885 after Géorge 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 Károly Zipernowsky, Ottó Bláthy and Miksa Déri at the Ganz company in Budapest in 1885, who créated the efficient "ZBD" modél 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.

Many others have patents on transformers.