GATE 2021 EE – Question 55
An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of $0.08\ \Omega$ per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor circuit to achieve maximum torque at start is ________ $\Omega$. (Round off to 2 decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.
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Correct answer: 0.50 to 0.54
Explanation
The synchronous speed is $\frac{120\times50}{8}=750$ rpm, so the slip at maximum torque is $s_m=\frac{750-650}{750}=0.1333=\frac{R_2}{X_2}$. So $X_2=\frac{0.08}{0.1333}=0.6\ \Omega$. Maximum torque at start needs $R_2+R_{ext}=X_2$, so $R_{ext}=0.6-0.08=0.52\ \Omega$.