A $1/3-$hp$,120-$V$,60-$Hz$,$ single$-$phase, capacitor$-$run, single$-$phase induction motor has two identical windings set $90$o apart in the motor housing. Each winding draws $7$A at $64$ lag when the rotor is locked. This is with no added capacitors, so the motor would have to be started by hand.

a$)$ Find the ideal capacitor to place in series with one of the windings at startup. Note: the ideal capacitor would create the ideal phase difference between the winding currents.

b$.)$ Each winding uses $141$W at pf $=0\mathrm{.}85$ when the motor is running at its rated speed. This is with no added capacitors, so the motor would have to be started by hand. Find a different capacitor to replace the capacitor of part a$).$ Choose this capacitor to make the current magnitude in the two windings exactly the same at rated speed. $($Don$\text{'}$t worry about the phase angles.$)$ V $=120$V$,$ P$=141$W$,$ and pf$=0\mathrm{.}85.$

The answers are:

a$.)140$ micro$-$farads

b$.)29$ micro$-$farads