A $10000$kVA,$3-$phase, star connected $11000V,2-$ pole turbo generator has a synchronous impedance of $(0\mathrm{.}0145+j0\mathrm{.}5)$ phase. The various losses in this generator are as follows:

Open circuit core loss at $11000V=92kW$

Windage and frietion losses $=55kW$

Short circuit load losses at rated current $=220kW$

Field winding resistance $=3,$ Field current $=175A.$

Ignoring the change in field current, compute:

i$.$ Efficiency at rated load at $0\mathrm{.}9$ PF lagging

ii$.$ Efficiency at $75\%$ rated load at $0\mathrm{.}8$ PF leading

iii. Maximum efficiency at rated load at unity PF