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A transformer has two coils wound over a core. Depending on use, the two coils are named primary and secondary coils. The primary and secondary coils are linked magnetically (not electrically except in case of auto Transformers) called mutual coupling. When the primary coil is excited with alternating voltage(A.C), varying magnetic flux is produced which links with the secondary coil and thus a voltage is induced in the secondary coil. Since there is no rotating or moving part utilized for the above process hence transformer is called a static device.

The word static used here should not be confused for static charges. It only signifies "not moving"

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Q: Why transformer is called static device?
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