Discussion
The eddy current loss in a dc machine varies with the thickness (t) of laminations as __________.
Answer: D
The eddy current loss varies as \(t^{2}\).
The eddy current loss in a laminated core is
\[ P_{e} = K_{e} B_{m}^{2} f^{2} t^{2} V \]
where \(B_{m}\) is the peak flux density, \(f\) the frequency, \(t\) the lamination thickness and \(V\) the core volume. Halving the thickness cuts the loss to a quarter, which is why armature and transformer cores are built from thin insulated laminations.
The loss grows with thickness, so \(1/t\) and \(1/t^{2}\) have the relationship upside down, and a linear dependence on \(t\) understates it.
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