A $3-$$,50-$Hz induction motor with its rotor star$-$connected gives $500$ V $($r$.$m$.$s$.)$ at standstill between slip$-$rings on open circuit. Calculate the current and power factor in each phase of the rotor windings at standstill when joined to a star$-$connected circuit, each limb of which has a resistance of $10$ and an inductance of $0\mathrm{.}03$ H$.$ The resistance per phase of the rotor windings is $0\mathrm{.}2$ and inductance $0\mathrm{.}03$ H$.$ Calculate also the current and power factor in each rotor phase when the rings are short circuited and the motor is running with a slip of $4$ per cent.