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GATE 2022 EE – Question 62

Electrical Machines · DC machines: separately excited, series and shunt, motoring and generating mode of operation and their characteristics, speed control of dc motors · 2 marks · Numerical answer

A 280 V, separately excited DC motor with armature resistance of $1\ \Omega$ and constant field excitation drives a load. The load torque is proportional to the speed. The motor draws a current of 30 A when running at a speed of 1000 rpm. Neglect frictional losses in the motor. The speed, in rpm, at which the motor will run, if an additional resistance of value $10\ \Omega$ is connected in series with the armature, is ________. (round off to nearest integer)

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Correct answer: 483

Explanation

At 1000 rpm, $E_b=280-30\times1=250$ V, so $E_b=0.25N$. The torque is proportional to the armature current and the load torque to speed, so $I_a=0.03N$. With the extra resistance, $280=E_b+11I_a=0.25N+11\times0.03N=0.58N$, so $N=\frac{280}{0.58}=482.8\approx483$ rpm.