A $Y-$connected, $3-$phase synchronous motor has a per$-$phase voltage of $125$ V and a synchronous reactance of $5.$ Suppose that the motor input power is $6$ kW and the power angle is $27.$

$($a$)$ Determine the per$-$phase power.

$($b$)$ Determine the terminal voltage.

$($c$)$ Determine the stator current, $I_a.$

$($d$)$ Determine the power factor.

$($e$)$ Draw the phasor diagram for the motor.

PLEASE ANSWER ALL PARTS