List of top Electrical Machines Questions on Three phase induction motors

A 4-pole induction motor with inertia of 0.1 kg-m\(^2\) 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, 4-pole, 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 Hz, three-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 \(\underline{\hspace{3cm}}\) \(\Omega\). (Round off to 2 decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.