A $$dc$$ series motor is rated $$230V,$$ $$1000$$ $$rpm,$$ $$80$$ $$A$$ (refer to Figure). The series field resistance is $$0.11\,\Omega ,$$ and the armature resistance is $$0.14\,\Omega .$$ If the flux at an armature current of $$20A$$ is $$0.4$$ times of that under rated condition, calculate the speed at this reduced armature current of $$20$$ $$A.$$

A separately excited $$DC$$ shunt motor is driving a fan load whose torque is proportional to the square of the speed. When $$100$$ $$V$$ are applied to the motor, the current taken by the motor is $$8$$ $$A,$$ with the speed being $$500$$ $$rpm.$$ At what applied voltage does the speed reach $$750$$ $$rpm$$ and then what is the current drawn by the armature? Assume the armature circuit resistance to be $$1\,\,\,\Omega .$$ Neglect brush drop and mechanical losses.

A $$DC$$ shunt generator delivers $$60$$ $$KW$$ at $$240$$ $$V$$ and $$360$$ $$rpm.$$ The armature and field resistances are $$0.015\,\,\,\Omega $$ and $$60\,\,\,\Omega $$ respectively. Calculate the speed of the machine running as a shunt motor and taking $$60$$ $$KW$$ input at $$240$$ $$V.$$ Allow $$1$$ volt per brush for contact drop.

A $$200V$$, $$10$$ $$kW$$ lap-wound $$d.c.$$ generator has $$10$$ poles and $$500$$ conductors on it's armature. If the pole face covers $$80\% $$ of the pole pitch, the pole face conductors required to fully compensate for armature reaction will be ___________________ conductors/pole.