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The area of the hysteresis loop of a core material (the loss per cycle) is 50 J/m³. Which value is closest to the hysteresis loss when a core of volume 0.010 m³ is used at 50 Hz AC?

  1. AAbout 0.5 W
  2. BAbout 25 W
  3. CAbout 2.5 kW
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Answer: B. About 25 W

The hysteresis loss is the loss per cycle (loop area) × frequency × volume: P = 50 J/m³ × 50 s⁻¹ × 0.010 m³ = 25 W. About 0.5 W forgets to multiply by the frequency; it is the energy per cycle, 0.5 J. About 2.5 kW forgets to multiply by the volume, and its proper unit would be W/m³. Hysteresis loss is proportional to frequency and eddy-current loss roughly to the square of frequency, so power supplies and motors operating at high frequencies use high-resistivity materials such as ferrites or thin laminated steel sheet. The unit of B-H loop area, T·A/m, is equal to J/m³.

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