$(10$ Points in Total$)-$A no$-$load test conducted on a $)=(746W,440-V,3-$phase,$60-Hz,$ squirrel$-$cage induction motor yielded the following results:

No$-$load voltage $($line$-$to$-$line$)$: $440$ V

No$-$load current: $14$ A

No$-$load power: $1,470$ W

Resistance measured between two terminals: $0\mathrm{.}5$

The locked$-$rotor test, conducted at reduced voltage, gave the following results:

Locked$-$rotor voltage $($line$-$to$-$line$)$: $163$ V

Locked$-$rotor power: $7,200$ W

Locked$-$rotor current: $60$ A

a$)$ Determine the equivalent circuit of the motor$-$please consider any rational, practical situation needed $(5$ points$).$

b$)$ Based on the equivalent circuit extracted in part $a)$ and using circuit analysis calculations, calculate the slip amount at which the maximum torque is being generated$-$i$.$e$.,s_b,$ slip at breakdown torque$-$and the breakdown torque $(5$ points$).$