As far as I understood, there are 2 Models for electric circuits that aim to simplify Maxwells Equations (by reducing the number of degrees of freedom from infinite field-values to 2 variables (voltage and current) per circuit element).
I'm however confused about how these models are obtained from Maxwells Equations:
The lumped-circuit model is obtained by assuming the following approximations:
- No change of magnetic flux in every loop of the circuit
- No change of charge in every element of the circuit
- Only Wavelengths that larger then the whole circuits dimensions
- Radiation effects are ignored
I'm especially worried about the 4th point: What does it mean to ignore radiation? Obviously we don't ignore induction effects in coils.
The 2nd point doesn't seem as understandable as well: Imagine a capacitor, and a voltage U that drops across it's plates. The conductors that connect the capacitors plates have the same potential as the respective plates. I now have a hard time imagining that the charge density inside the conductors doesn't change at all when the voltage drop across the capacitor changes. Of course the change density doesn't change enough to affect any electric fields in the lumped circuit model, but it still changes.
What's even more confusing is that the transmission-line model is not deduced from maxwells equations, but instead built up from the lumped-circuit model. I'd like to know what the limitations of this model are, but it seems very complicated to estimate this.
I think all in all my questions can be boiled down to "What are the field equations that hold in the lumped circuit model"? Are there terms originating in Maxwells Equations that are completely ignored? Are there some that are approximated just to quadratic order? Or to linear order? Does the constant c play a role here?