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Assuming the coils have the same numbers of turns of wire ( and hence should produce the same instenity of magnetic feild ) the coil that heats up may have a higher magnetic reluctance, hence dissapates more of the magnetic energy as heat. Examine the cores closely , laminated cores ( one made of plates ) tend to have a lower magnetic reluctance.

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Q: Why will one soft iron core in a coil heat up while another similar core with same coil and current not heat up. Could this problem be due to the AC frequency?
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