With reference to a three$-$phase cage rotor induction motor:

$($a$)$ explain why the rotor power factor is very low at start;

$($b$)$ explain why the rotor core losses are negligible when the motor is running;

$($c$)$ sketch and label a typical torque$/$speed characteristic and indicate:

starting torque;

pull$-$out torque;

synchronous speed.

$($d$)$ explain, with the aid of a labelled sketch, how a shaped, deep$-$bar rotor design increases starting torque;

$($e$)$ state ONE additional advantage of a shaped, deep$-$bar rotor.