GATE 2024 EE – Question 54
A 3-phase star connected slip ring induction motor has the following parameters referred to the stator:
$R_s=3\ \Omega,\ X_s=2\ \Omega,\ X_r'=2\ \Omega,\ R_r'=2.5\ \Omega$
The per phase stator to rotor effective turns ratio is 3:1. The rotor winding is also star connected. The magnetizing reactance and core loss of the motor can be neglected. To have maximum torque at starting, the value of the extra resistance (referred to the rotor side) to be connected in series with each phase of the rotor winding is __________ (rounded off to 2 decimal places).
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Correct answer: 0.27 to 0.29
Explanation
With stator resistance included, maximum torque occurs at the slip where the total rotor resistance referred to the stator equals $\sqrt{R_s^2+(X_s+X_r')^2}=\sqrt{9+16}=5\ \Omega$. For maximum torque at starting ($s=1$) the total referred rotor resistance must be 5 Ω, so the extra resistance referred to the stator is $5-2.5=2.5\ \Omega$. Referred to the rotor side (turns ratio 3), it is $\dfrac{2.5}{3^2}=0.28\ \Omega$.