Discussion
A dc generator driven at half its rated speed with rated field current generates
Answer: B
Correct answer: about half its rated emf
The emf is proportional to speed at constant flux, so half the speed gives half the emf. The relation is linear, not square-law, because it is the rate of cutting flux that generates the voltage - the quarter answer confuses this with an energy quantity. This is also why a self-excited machine has a critical speed: below it the magnetisation curve falls too low to meet the field resistance line.
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