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A 3 phase, 50 Hz, six pole induction motor has a rotor resistance of 0.1 Ω and reactance of 0.92 Ω. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3%, the ratio of maximum torque to full load torque is

1. (A) 1.567
2. (B) 1.712
3. (C) 1.948
4. (D) 2.134

Correct answer: (C) 1.948

Solution

Slip at max torque s_m=R2/X2=0.1/0.92=0.1087. Tmax/Tfl=(s_fl^2+s_m^2)/(2*s_fl*s_m)=(0.0009+0.01181)/(2*0.03*0.1087)=0.01271/0.006522=1.95. So the ratio is about 1.948.

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