# How is an inductor a lumped element?

While learning the Lumped Circuit Abstraction (and the Lumped elements discipline), an inductor was considered a lumped element. But I fail to see how it fits the requirements of LCA:

1. For it, the $\frac{d\phi}{dt}$ is not zero.
2. In a circuit with an inductor, (in AC supply), resistances would not be the only irreversible energy loss, owing to the inductor's em waves.

Although there are various ways to put in the restrictions after which LCA is rendered valid, but these two requirements are commonly cited.

• All lumped elements are unrealistic perfect models. – PlasmaHH Jan 27 '17 at 10:56
• But even for a perfect inductor, would not the rate of change of flux be non-zero? – Satwik Pasani Jan 27 '17 at 11:03
• @PlasmaHH: that's not answering the questions. Although it is a model it is satisfied to a very very large extent in very very many practical cases; namely in all cases where it makes sense to work with a circuit diagram (with extensive quantities contained in ODEs) instead of Maxwells Equations (with intensive quantities contained in PDEs). The latter one is much more difficult. – Curd Jan 27 '17 at 11:57

I.e. the requirement for good lumped circuit element approximation is that $\frac{d\Phi}{dt} =0$
The same is the case for $\frac{dq}{dt}$: