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When deriving formulae for RC, RLC, LC circuits, etc., we typically assume that current is steady. Griffiths gave a good explanation of why this assumption is reasonable (he states essentially that nonsteady current forces itself to become steady through electric forces). However, it seems that we also assume a non changing magnetic field when we apply “Kirchhoff's loop rule.” But current of course varies, so the magnetic field changes, and thus the electric field has some curl. So I’m not sure why this assumption is justified. Is the curl of the field negligible, and does the rule hold true practically? If so, why? Edit: I’ve realized that we’re essentially assuming the circuit itself has no inductance; all inductance comes from an inductor that could be present. In addition, the induced forces act only within the inductor itself (so that the voltage drop across the inductor is the emf). Am I correct in this?

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  • $\begingroup$ In the voltage source is constant eventually it will all be steady, if the source varies then the signal is a fusion of time. $\endgroup$ – PhysicsDave Dec 5 '18 at 16:18
  • $\begingroup$ Concerning your edit: yes, that's correct. Usually it's a pretty good assumption, though there might be situations where you have to (or want to) take it into account (e.g., loop antennas.) Whether there are other important exceptions might be a good question for Electronics StackExchange. $\endgroup$ – Michael Seifert Dec 5 '18 at 16:21
  • $\begingroup$ Key point in my answer to the first linked question above: We typically restrict lumped circuit analysis to cases where the largest dimension of the circuit is less than 1/10 of the wavelength associated with the highest signal frequency present in the circuit. $\endgroup$ – The Photon Dec 5 '18 at 17:16
  • $\begingroup$ Thanks for the explanations/clarifications. I’ll have to look into physicsdave’s point. $\endgroup$ – Arjun Puri Dec 5 '18 at 17:21
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Inductance is a property of the conducting wire just like capacitance is a property of a conductor. For a general wire which may be stretched out very long, the actual area it encloses in the loop is so large that inductance is negligible. When we create these circuits, we essentially make this assumption but in practical scenarios, this does somewhat have to be accounted for.

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