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GATE 2022 EE – Question 65

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 3-phase, 415 V, 4-pole, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase autotransformer. If the magnetizing impedance of the induction motor and no load current of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ________. (round off to two decimal places).

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Correct answer: 0.62 to 0.64

Explanation

With a tap ratio $x$ the motor sees $xV$ and draws $5xI_r$, and the line current is reduced by another factor of $x$: $I_{line}=5x^2I_r$. Setting $5x^2=2$ gives $x=\sqrt{0.4}=0.63$.