A three$-$phase, eight$-$pole, $60-$Hz$,4160-$V$,1000-$kW squirrel$-$cage induction motor has the following

equivalent$-$circuit parameters in ohms per phase Y referred to the stator:

$1=0\mathrm{.}220,2=0\mathrm{.}207,1=1\mathrm{.}95,2=2\mathrm{.}42=45\mathrm{.}7$

a$)$ State the input power and the output power of the system.

b$)$ Calculate the copper loss of the system.

c$)$ Calculate the efficiency of the induction motor.