A 3 phase , 6 pole , 400 V , 50 Hz , induction motor has R2= 0.1 ohm /ph , X2= 0.8 ohm /ph and the induced emf between slip rings at standstill is 160 V , Assume the friction losses is 300 W. find :- a) the torque output at slip =3% . b) critical slip and the torque maximum .

On full-load a 300 V series motor takes 90A and runs at 15 rev/s. The armature resistance is 0.1 ohm and the series winding resistance is 50 m.Determine the speed when developing full load torque but with a 0.2 ohm diverter in parallel with the field winding. (Assume that the flux is proportional to the field current.