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GATE 2022 EE – Question 63

Electrical Machines · Three-phase induction machines: principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control · 2 marks · Numerical answer

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)

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Correct answer: 1733

Explanation

The speeds are $\omega_1=104.72$ and $\omega_2=157.08$ rad/s. The gain in kinetic energy is $\frac12J(\omega_2^2-\omega_1^2)=0.05\times(24674-10966)=685$ J. The load energy over the 4 s is $T_L\times\omega_{avg}\times t=2\times130.9\times4=1047$ J. The total energy is $685+1047=1733$ J.