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Then I asked myself, why can't we use these equivalent formulas for power (IV and V^2/R)??

I tried to use them but they gave me different values for power loss

I searched for an answer here and I discovered that the supply voltage is not equal to the drop voltage through the resistance in the secondary coil.

So IV and V^2/R works when V is the drop voltage..

After that I had another question, How can we apply Kirchhoff's voltage law in the secondary coil?

Due to KVL the sum of voltages must equal zero.

But appearantly, that doesn't exist in the secondary coil as long as the drop voltage is not equal to the supply voltage..

Any one has an explanation?