# Are we always allowed to treat an inductor as a battery with the same voltage?

When there is an induced emf, Kirchhoff's Loop Rule no longer is true, because electric fields are nonconservative when there is an induced current, as stated by Faraday's Law:

However, I have seen explanations that incorporate inductors and induced emfs into circuit analysis by treating them like batteries. For example, for the following circuit, if V is the voltage of the battery, Vinduced is the induced emf from the inductor, R is the resistance of the resistor, and I is the current, then V - Vinduced = IR:

To me, this seems to be treating the inductor like a battery with voltage Vinduced. I see why this is justified; the only difference between the electric field created by a battery and by an inductor is that the inductor's field is nonconservative, while the battery's field is conservative due to the electric field inside the battery. However, are there any cases where an inductor acts differently than a battery with the same voltage, at least for circuit analysis purposes?

• "Are there any cases where an inductor acts differently than a battery with the same voltage, at least for circuit analysis purposes?" Most cases because it's an inductor not a battery. With no forward EMF, if you treated an inductor as a source it would be a current source, not a voltage source. And this would only be valid for an instant in time. Then of course, there are all the times where it's not a source. Commented Jul 19, 2022 at 13:31
• Inductors have transient effects, batteries don't. Commented Jul 19, 2022 at 13:31