The GATE Grind

GATE 2025 EE – Question 44

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 · Multiple choice

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume linear magnetic circuit. The external resistance, in Ω, that must be connected in series with the armature to reduce the speed of the motor by half, is closest to

  1. 23.28
  2. 4.82
  3. 46.7
  4. 0

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) 23.28

Explanation

For a series motor with a linear magnetic circuit, $\phi\propto I$, so $T\propto I^2$ and $E\propto\omega I$. The load torque is $T_L\propto\omega^3$, so $I\propto\omega^{3/2}$. At half speed, $I'=40\times0.5^{1.5}=14.14$ A and, since the resistance is negligible at the start ($E=400$ V), $E'=400\times0.5\times0.3536=70.71$ V. Then $400=70.71+14.14R_{ext}$ gives $R_{ext}=23.28\ \Omega$.