GATE 2025 EE – Question 35
The induced emf in a 3.3 kV, 4 pole, 3-phase star connected synchronous motor is considered to be equal and in phase with the terminal voltage under no load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of 2° mechanical with respect to the terminal voltage phasor. If the synchronous reactance is 2 Ω, and stator resistance is negligible, then the motor armature current magnitude, in ampere, during loaded condition is closest to ____________ (round off to two decimal places).
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Show answer and explanation
Correct answer: 66.16 to 66.82
Explanation
With 4 poles, the electrical angle is $\delta=\dfrac P2\times2^\circ=4^\circ$. The phase voltage is $V_{ph}=3300/\sqrt3=1905.3$ V, and $|E|=|V|$. The phasor difference is $|V-E|=2V_{ph}\sin\dfrac\delta2=2\times1905.3\times\sin2^\circ=132.98$ V. The armature current is $I_a=\dfrac{132.98}{X_s}=\dfrac{132.98}{2}=66.49$ A.