(1) $\eta = \dfrac{xP}{xP+W_i+x^2W_c} = \dfrac{P}{P+W_i/x+xW_c}$

for more $\eta$, $\dfrac{d\eta}{dx} =0$

$\therefore \dfrac{d\eta}{dx} = -\dfrac{P}{(P+W_i/x+xW_c)^2}.\left ( -\dfrac{W_i}{x^2}+W_c \right ) =0$

$\therefore \frac{-W_i}{x^2}+W_c =0 \Rightarrow W_i =x^2W_c$   ........ Condition for $\eta _{max}$

$\therefore \eta_{max}= \dfrac{xP}{xP+2W_i}$

(2) At $\eta _{max}$,

$x=\sqrt{\dfrac{W_i}{W_c}}$

x $\rightarrow$ Load; $\eta$ $\rightarrow$ efficiency; $W$$\rightarrow$ $I_{ron} loss$

$W_c \rightarrow Cu$ loss; P $\rightarrow$ full load kVA