Question $4$ A $6-$pole $3-$phase $50$ Hz induction motor with a star$-$connected rotor has a resistance per phase of $0\mathrm{.}25$ and at standstill the reactance per phase is $1\mathrm{.}2.$ The measured emf between the slip rings at standstill is $120$ V$.($a$)$ List $3$ advantages of $3-$phase induction motors over single$-$phase motors. $[3$ marks$]($b$)$ For a full$-$load speed is $960$ rpm$,$ calculate the following quantities: $($i$)$ the motor slip and the $[3$ marks$]($ii$)$ the voltage induced in each phase of the motor $[3$ marks$]($iii$)$ the rotor reactance per phase $[2$ marks$]($iv$)$ the rotor current and power factor $[5$ marks$]($c$)$ Calculate what value of resistance would need to be added in series with the slip rings at start up to limit the rotor starting current to $30$ A$.[4$ marks$]$ Assume the rings are short$-$circuited at full$-$load.