GATE 2021 EE – Question 54

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 belt-driven DC shunt generator running at 300 RPM delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. If the armature resistance is $0.025\ \Omega$, field resistance is $50\ \Omega$, and brush drop is 2 V. Ignoring armature reaction, the speed of the motor is ________ RPM. (Round off to 2 decimal places.)

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Correct answer: 273.00 to 277.00

Explanation

Field current $I_f=\frac{200}{50}=4$ A. As a generator, $I_L=500$ A and $I_a=504$ A, so $E_g=200+504\times0.025+2=214.6$ V at 300 rpm. As a motor, $I_L=\frac{10000}{200}=50$ A and $I_a=46$ A, so $E_b=200-46\times0.025-2=196.85$ V. The flux is unchanged, so $N=300\times\frac{196.85}{214.6}=275.2$ rpm.