The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:
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where VS is the instantaneous voltage, NS is the number of turns in the secondary coil and Φ equals the magnetic flux through one turn of the coil.
The voltage induced across the primary coil:
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where VP is the instantaneous voltage, NP is the number of turns in the primary coil and Φ equals the magnetic flux through one turn of the coil.
Taking the ratio of the two equations for VS and VP gives the basic equation for stepping up or stepping down the voltage
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This is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit in order to produce an electromotive force and the phenomenon is called electromagnetic induction.The law states that the induced electromotive force in any closed circuit is equal to the negative of the rate of change of the magnetic flux which is enclosed by the circuit.

INDUCTION LAW

Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon called electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.In 1831, Michael Faraday, an English physicist gave one of the most basic laws of electromagnetism called Faraday's law of electromagnetic induction. This law explains the working principle of most of theelectrical motors, generators, electrical transformers and inductors . This law shows the relationship between electric circuit and magnetic field. Faraday performs an experiment with a magnet and coil. During this experiment, he found how emf is induced in the coil when flux linked with it changes. He has also done experiments in electro-chemistry and electrolysis.