A $120-$V$,60-$Hz$,$ two$-$pole, permanent$-$split$-$capacitor, single$-$phase induction

motor has a rated output power of $500$ W$.$ When operated at its rated voltage

and load with an auxiliary$-$winding capacitance of $41\mathrm{.}3$ F$,$ the main$-$winding

current is observed to be $4\mathrm{.}89$ A at a phase angle $($with respect to the applied

voltage$)$ of $55\mathrm{.}8$ and the auxiliary$-$winding current is observed to be $3\mathrm{.}32$ A

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Calculate the motor power input, power factor, and efficiency.

Calculate the impedances Z main and Z aux of the main and auxiliary windings.

The main and auxiliary windings differ only in their number of turns. The main winding has $180$ turns$/$pole$.$ Calculate the turns$/$pole of the auxiliary winding.

Show that under this operating condition, the combined mmfs of the main

current which will lag that of the main winding by $90.$ Exercise your program

at a phase angle of $34\mathrm{.}2.$