Discussion
A dc motor's efficiency is greatest when
Answer: C
Correct answer: the copper loss equals the constant loss
Writing the efficiency with constant loss \( W_c \) and variable loss \( I^2R \) and differentiating with respect to current gives the maximum at
\[ I^2R = W_c \]Machines are designed so that this occurs somewhat below rated load, near where they will spend most of their working life. It is not at full output, and certainly not at no load, where there is no output at all to be efficient with.
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