A three phase 415 V, 50 Hz, 6-pole, 960 RPM, 4 HP squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the supply voltage and frequency are reduced by 20%, the resultant speed of the motor in RPM (neglecting the stator leakage impedance and rotational losses) is ___________ (Round off to the nearest integer).

A 4-pole induction motor with inertia of 0.1 kg-m² drives a constant load torque of 2 Nm. The speed of the motor is increased linearly from 1000 rpm to 1500 rpm in 4 seconds as shown in the figure below. Neglect losses in the motor. The energy, in joules, consumed by the motor during the speed change is _________. (round off to nearest integer).

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.