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GATE 2025 EE – Question 26

Electrical Machines · DC machines: separately excited, series and shunt, motoring and generating mode of operation and their characteristics, speed control of dc motors · 1 mark · Multiple choice

The operating region of the developed torque ($T_{em}$) and speed ($\omega$) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque ($T_L$) characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S. Which one of the following trajectories will take the shortest time?

Diagram for GATE 2025 EE question 26
  1. O − Q − R − S
  2. O − P − S
  3. O − E − S
  4. O − F − S

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Show answer and explanation

Correct answer: (A) O − Q − R − S

Explanation

The acceleration is $\dfrac{T_{em}-T_L}{J}$, so the fastest way to reach S is to apply the maximum available torque throughout. That means going from O straight up to the maximum torque Q, then along the maximum-torque boundary QR to the maximum speed, and only then coming down to S. So the trajectory is O − Q − R − S.