GATE 2024 EE – Question 55
A 5 kW, 220 V DC shunt motor has 0.5 Ω armature resistance including brushes. The motor draws a no-load current of 3 A. The field current is constant at 1 A. Assuming that the core and rotational losses are constant and independent of the load, the current (in amperes) drawn by the motor while delivering the rated load, for the best possible efficiency, is ________ (rounded off to 2 decimal places).
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Correct answer: 37.09 to 37.47
Explanation
At no load the input power is $220\times3=660$ W, of which the armature copper loss is $(3-1)^2\times0.5=2$ W. The remaining 658 W (field loss 220 W plus core and rotational loss 438 W) is constant. Efficiency is maximum when the variable (armature copper) loss equals the constant loss: $I_a^2\times0.5=658$, so $I_a=36.28$ A. The line current is $I_a+I_f=36.28+1=37.28$ A.