A 3-phase, 415 V, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ________. (round off to two decimal places).
An 8 pole, $50 \mathrm{~Hz}, 3$ phase, slip-ring induction motor has an effective rotor resistance of $0.08 \Omega$ per phase. Its speed at maximum torque is 650 rpm . The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is $\_\_\_\_$ $\Omega$. (Round off to 2 decimal places). Negleet magnetizing eurrent and stater leakage impedanee. Consider equivalent eireuit parameters referred to stator.
R1 = R2' = Xl1 = Xl2' = 12 $$\Omega $$, Xm = 240 $$\Omega $$
and s is the slip. At no-load, the motor speed can be approximated to be the synchronous speed. The no-load lagging power factor of the motor is___________ (up to 3 decimal places).
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