Why when p copper=p core maximum efficiency occurs for the transformer?

• Condition for maximum efficiency of transformer can be obtained by differentiating the efficiency equation of the transformer with respect to the load factor

• load factor can be defined as the ratio of operating load of transformer by full load of transformer

By solving, we get
P core loss = square of load factor *pcopper loss
From the above equation it can be defined as the maximum efficiency of the transformer occurs at a load factor at which the iron losses is equal to copper losses.
The efficiency of the transformer changes with the load . The efficiency of the transformer will be maximum at certain load when the copper losses is equal to the core losses i.e, maximum efficiency of the transformer will be attained when the copper losses at particular load should be equal to the no load losses.

prove the maximum efficiency of the transformer... Reply plz