GATE EE 2024 Set 1 — Question 55
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Electrical Machines → DC Machines → Losses & Efficiency
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Question
A 5 kW, 220 V DC shunt motor has 0.5 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).
Correct answer
27.19 to 27.39
Solution
Given: rated output W, V, , no-load line current A, field current A (constant).Step 1 — constant losses.
No-load armature current: A.
At no load the armature input covers the armature copper loss plus the core and rotational losses, soField (shunt) loss: W.Step 2 — power balance at rated load.
Let be the line current drawn. Then , andStep 3 — solve.Step 4 — choose the root giving the best efficiency.
Both roots deliver the rated 5 kW, but the larger current implies an enormous armature copper loss. The smaller root has the smaller total loss and hence the better efficiency:(the other root would give ).Answer: A
No-load armature current: A.
At no load the armature input covers the armature copper loss plus the core and rotational losses, soField (shunt) loss: W.Step 2 — power balance at rated load.
Let be the line current drawn. Then , andStep 3 — solve.Step 4 — choose the root giving the best efficiency.
Both roots deliver the rated 5 kW, but the larger current implies an enormous armature copper loss. The smaller root has the smaller total loss and hence the better efficiency:(the other root would give ).Answer: A
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