GATE 2026 EE – Question 59

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 balanced three-phase supply is given to a 30 kW, 4-pole, 400 V, 50 Hz, wound rotor induction motor with Y-connected stator and rotor windings. The motor is driving a constant torque load. With shorted slip-rings, the machine runs at 1476 rpm.

When an external non-inductive resistance of 0.27 Ω per phase is connected in series in the rotor circuit, the steady-state speed drops to 1404 rpm.

Neglecting rotational losses, the actual per phase rotor winding resistance is ____ Ω.

(Round off to two decimal places)

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Correct answer: 0.08 to 0.10

Explanation

The synchronous speed is $N_s=\dfrac{120\times50}{4}=1500$ rpm. The slips are $s_1=\dfrac{1500-1476}{1500}=0.016$ and $s_2=\dfrac{1500-1404}{1500}=0.064$. For constant torque (constant rotor current for the same flux), $\dfrac{R_2}{s}$ stays constant: $\dfrac{R_2}{0.016}=\dfrac{R_2+0.27}{0.064}$, so $4R_2=R_2+0.27$ and $R_2=0.09\ \Omega$.