I'm sure the inductor model, i.e. vL(t) = iL'(t)*L follows without directly from Faraday's eq. But even there, with Faraday's equation we think of the changing magnetic field as inducing the voltage in the loop, where in the model it seems the other way around, that is, the voltage increases the current which increases the magnetic field. And, I'm pretty sure Ampere's equation leads to the capacitor model, i.e., vC'(t) = iC(t) / C. That is, I'm sure Ampere's equation gives the E field strength between the capacitor plates when the circuit is open, but when the circuit is closed I don't see how Ampere's equation leads to the electric field acting through the wire and moving the electrons. So, I'm asking about how to think about these things to better understand them.