Problem $3.$

A $3-$phase, $120-V($line$-$to$-$line$),60-Hz,Y-$connected induction motor has the following parameters: $R=R_2^{\text{'}}=0\mathrm{.}1,x_{eq}=1.$ The magnetizing inductance is very large and can be considered as infinity. At the rated load condition, the rotor mechanical speed is $1170$ rpm $.$

a$.$ Stator copper loss and rotor copper loss at the rated load condition.

b$.$ Maximum torque of this motor, and motor mechanical speed in rpm to yield the maximum output torque.

c$.$ Starting torque of this motor and starting current $($magnitude$)$

d$.$ Based on the torque you calculated for all the three speeds above $($starting$,$ maximum torque rated torque$),$ sketch a torque vs speed curve for this induction motor. The x $-$axis should be the mechanical speed of the motor in rpm$.$ The y $-$axis is torque in Nm $.$ Use the values you have got in previous problems to do the sketch. Label the mechanical speed value and torque value for the three operating points in your sketch, i$.$e$.,$ starting, maximum torque and rated torque.