A three phase synchronous motor connected to ac mains is running at full load and unity power factor. If its shaft load is reduced by half, with field current held constant, its new power factor will be

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