Yes, yes and yes... fyi its ohms law. Only so much current can be passed over a conductor of given density. Current is limited by resistance given constant voltage .. etc. Its a variable equation depending on one of the 3 factors involved. However, if you dont have locomotive force in the amount needed to feed what is demanded.. regardless the size of the conductor it aint gonna happen mang. 8ga is fine for anything up to 400w rms. I prefer overkill when it comes to wiring though.Normally, it is caused by running too thin of wire for the rated current. I forget the exact physics as to why it does this, I'm sure you can find it if you read around though a bit. Make sure you run the proper size wires and you should be okay. Otherwise, it's time for a big 3 upgrade (batt/alt/grounding).
I personally run 4Ga wire on everything. Single amp system.. 4Ga wire, I have yet to NOT see an improvement upon reinforcing the delivery of current (adding a cap). Side benefit of a capacitor is filtering ac current.. though the internals of modern amplifiers are good about noise reduction.. and modern day alternators are good about keeping ac to a minimum.. the cap still helps. Cars are very noisy electrical environments.
You're completely correct about the charging system needing to be upgraded. Most oem's skimp here so that it barely covers the vehicle load (cost cutting) However.. the amplifier manufacturers are also skimping on power supply caps to save costs and space. Its not just the constant supply from the vehicle that is the issue, its the ability to have enough on demand reserve to cover the amplifiers demands on sharp spikes. It has to come from somewhere.. Caps aren't a "might" work.. they do work. They are the instant current reserve the car doesn't have built into its charging system.
You took a amplifier design course..generally thats not for fun (though I'd find it fun ) I'm thinkin you're on a scholastic path that brings you more understanding here than most.. but to break it down to those that aren't as educated...
think of the electrical system like you would fuel injection (its really not exactly like this but its a good example for those that dont know better) ..
you have a fuel supply at a given pressure and volume (alternator) with a slow response reserve built in (lead acid battery) .. everything is good if you have a constant supply that meets a fairly constant demand (slow reserve covers any mild demand changes). Here's where it gets fun.. sharply open the throttle (represents amp yanking for power to produce a loud low note).. blahp.. goes lean.. system falls on its face but recovers once the pump and slow reserve catch up to the demand leveling out.
The cap acts like a larger fuel rail.. a reserve under pressure immediately responding to sharp changes.. when demand is instant and high.. it delivers before the rest of the system can fall short and replenishes quickly as the system stabilizes.
Basically how a stiffening cap works. Now electrical theory and ohms law play more detailed and important parts into that, but without getting exponentially more complicated thats a good description.
hehehe.. I can play this all day Electricity and I have long been friends. Its not touchy to me, I know they (caps) work. To a point though, you're right they aren't "needed" for a auto system .. but do have a nice effect when used correctly. Also much cheaper than a bat/alt upgrade.This is a pretty touchy subject, and I am just playing devils advocate with mango. I said -1 to even out the scale more so and let you know there is a debate on the subject.
Agree'd.. for some the integrated subs hit the spot. Def keep us posted.I think you'll enjoy your boss. It isn't going to be the top quality system out there, but it certainly will be better than what you have I bet. Should be enough to support your low end. It's a nice medium without going too far into the audio world in my opinion. Let us know how the install goes and how it sounds =)