$(15\text{'})$ Problem $3.$ A $3-$phase, $120-$V $($line$-$to$-$line$),60-Hz,Y-$connected induction motor has the following parameters: $R_1=R_2^{\text{'}}=0\mathrm{.}1,x_{eq}=1.$ The magnetizing inductance is very large and can be considered as infinity. At the rated load condition, the rotor mechanical speed is $1170$ rpm $.$

Calculate the following:

$(1\text{'})$ Draw the equivalent circuit you will use to solve this problem.

$(1\text{'})$ Number of poles for this induction machine.

$(1\text{'})$ Motor slip at the rated load condition and frequency of rotor current.

$(2\text{'})$ Under rated load, what's the rotor magnetic field rotating speed $($ rpm $)$ seen on the rotor? What's the rotor magnetic field speed $($ rpm $)$ seen on the stator?

$(2\text{'})$ Developed torque and developed power at the rated load condition.

$(1\text{'})$ Stator current magnitude at the rated load condition.