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GATE 2019 EE – Question 58

Electrical Machines · Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors · 2 marks · Numerical answer

A 220 V (line), three-phase, Y-connected synchronous motor has a synchronous impedance of $(0.25+j2.5)\ \Omega$/phase. The motor draws the rated current of 10 A at 0.8 pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is ________.

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Correct answer: 245

Explanation

The phase voltage is $\frac{220}{\sqrt3}=127.0$ V and the current is $10(0.8+j0.6)=8+j6$ A (leading). For a motor $E=V-Z_sI=127.0-(0.25+j2.5)(8+j6)=127.0-(-13+j21.5)=140.0-j21.5$ V, so $|E|=141.7$ V per phase and the line value is $\sqrt3\times141.7=245$ V.