About Transformer Equivalent Circuit
The equivalent circuit will only be \$(\frac{N1}{N2})^2R_{load}\$ if it was an ideal transformer.
Real trasformers have nonideal components. For example, the joule loss on the widings, or the core hysteresis. Those phenomena produce several effects, that must be accountable, in order to get the accurete equivalent circuit.
I sugest the reading Electric Machinery Fundamentals by Stephen Chapman, to better understand how to experimentally obtain your transformer's equivalent circuit.