A $3$phase, $400$ V$,50$ Hz$,960$ rpm$,6$ pole $,$ star connected, wound rotor induction motor has the following parameters per phase referred to the stator. Rs $=0\mathrm{.}3$W$,$ Rr$=0\mathrm{.}5$W$,$ X$1=$ X$2=1\mathrm{.}6$W$,$ Xm$=35$W$.$ Stator to rotor turns ratio is $2.$ The motor speed is controlled by the static rotor resistance. The filter resistance is $0\mathrm{.}01$W$.$ The value of the external resistance is chosen such that a$=0,$ the break$-$down torque is obtained at standstill. Determine the value of external resistance.