Answer: In order to get the answer that why core loss is constant in a transformer, first take a look on this formula
Iron Losses = (Kh x Phi^1.2 x F) Watt/M^3
Where Kh – Hysteresis Constant
Phi – Flux
F – Frequency
in above equation Kh, F are constant & Phi increase only 1 to 5% from No load to full Load. Hence Iron Losses are practically constant at all loads.
Although, these losses are voltage dependent and voltage is almost constant from no load to full load. that is why core losses are also almost constant in a transformer.
Out of these losses core loss is constant whereas copper loss is variable. The reason behind core loss being constant is that hysteresis loss and eddy currentloss both are dependent on the magnetic properties of the material used in the construction and design of the core of the transformer.