$5\mathrm{.}40.$ A $\backslash (50-\backslash$mathrm$\{$kW$\},250-\backslash$mathrm$\{$V$\},600-\backslash$mathrm$\{$rpm$\}\backslash ),$ long$-$shunt compound generator equipped with a field diverter resistance delivers the rated load at the rated voltage. The armature and series field resistances are $\backslash (0\mathrm{.}05\backslash$Omega $\backslash )$ and $\backslash (0\mathrm{.}01\backslash$Omega $\backslash ),$ respectively. There are $100$ turns per pole in the shunt field winding and $2$ turns per pole in the series field winding. The rotational loss is $4\mathrm{.}75$ kW $.$ The measured currents through the shunt field winding and the diverter resistance are $5$ A and $41$ A $,$ respectively. Determine $($a$)$ the series field current, $($b$)$ the diverter resistance, $($c$)$ the efficiency, and $($d$)$ the torque applied by the prime mover.