Well Paul, I think it is a pure shame if you haven't had the chance to teach in the past because I know you would be fantastic at it! I would add that the the amount of parallel resistance effects what they call the Q, or Quality Factor of the resonant circuit. You will hear the term, "3dB bandwith" for power, or "6dB bandwidth" for voltage, or "half power point". Adding that parallel resistance is one way to broaden response. Another common way is to combine LC networks that are tuned towards the high and low ends of a desired bandwidth, or "stagger tuned" for a network. The areas where the response falls off on the sides are sometimes called "skirts", which got my attention.
Now, you also mentioned the network across a DC supply, which for most of the time would look like a short circuit.
As you get higher in frequency, everything gets interesting. The series inductance of capacitor leads starts showing up in a meaningful way, as does the capacitance between turns of an inductor. Look inside a UHF tuner if you want to see something that makes no sense if you're used to living in a low frequency world. I used to tune UHF diplexors, and to this day, have no clue as to how things I did to flatten response worked, just that they did work.
Joe
