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When a DC circuit is carrying current, large amounts or small, is there induced-emf due to the inductance? Or is it only applied to AC circuits?

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In the limit of long times, the currents are steady, so the magnetic fields they create are steady so there is no induced EMF. This situation is usually tagged "steady state".

That said, there will be a period of time when you have just switched a circuit on or off during which things have not settled down and then there will in general be effects not seen in the steady state (including induced EMFs). This is called the "transient" behavior.

Transient behavior analysis is a important component of electronics design.

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