A three-phase squirrel cage induction motor has a starting torque of $$150\% $$ and a maximum torque of $$300\% $$ with respect to rated torque at rated voltage and rated frequency. Neglect the stator resistance and rotational losses. The value of slip for maximum torque is

A $$100$$ $$kVA$$, $$415V,$$ star connected synchronous machine generates rated open circuit voltage $$415V$$ at a field current of $$15A.$$ The short circuit armature current at a field current of $$10A$$ is equal to the rated armature current. The per unit saturated synchronous reactance is

A single-phase $$50$$ $$kVA,$$ $$250$$ $$V/500V$$ two winding transformer has an efficiency of $$95\% $$ at full load, unity power factor. If it is reconfigured as a $$500V/750V$$ auto-transformer, its efficiency at its new rated load at unity power factor will be

The dc motor, which can provide zero speed regulation at full load without any controller is