The condition for maximum efficiency in transformer is

The transformer will give the maximum efficiency when their copper loss is equal to the iron loss.

Copper loss:

A loss in a transformer that takes place in the winding resistance of a transformer is known as the copper loss.

Copper loss = i2R

Iron loss:

Iron losses = Eddy current loss + hysteresis loss

Eddy current loss = Ke t2 f2 B2

Hysteresis loss = Kh f B^η

Where, K_e & K_h are constant

f = Supply frequency

B = Flux density

t = thickness

Efficiency is maximum at some fraction x of full load:

\(x = \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}}\)

Where Wi = iron losses

Wcu = copper losses

Load at maximum efficiency \(= Full\;load \times \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}} = Full\;load \times \sqrt {\frac{B}{A}} \)

kVA at maximum efficiency is given by,

\(kVA\;at\;{η _{max}} = full\;load\;kVA \times \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}}\)