A three phase, Y$-$ connected $480$V $($line to line$)30$hp$,6$ poles induction motor has the following equivalent circuit contains in Ohms per phase referred to the stator: R$1=030$ R$2=020$ X$1=16$ X$2=12$ Xm $=36$ The total friction, windage, core loss may be assumed to be constant at $1320$ Watts. The motor is connected directly to a $480$V source. $($a$)$ For a rated shaft output power of $30$hp$,$ what is the internal $($electromagnetic$)$ power in Watts. $($b$)$ Determine the slip and speed for the conditions in $($a$)$ using the simplified circuit with VTHRTH jXTH jX$2$R$2$ s $($c$)$ Determine the internal and output torque in Nm$.($d$)$ Determine the phase current, terminal power factor, input power and efficiency