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Why does the voltage induced in the secondary coil of a transformer lag 90 degrees from the flux in the core? The secondary voltage is induced when the flux cuts it, but then, why does the induced voltage in the secondary lag 90 degrees behind the flux?

What is the reason behind it?

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Because of the laws of induction, V = -N dφ/dt. Notice the d/dt bit? That naturally shifts a sine wave by 90 °

In other words, the secondary induced voltage is proportional to the rate of change of magnetic flux and, the number of turns.

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