Of course the cap recharges off of the battery //content.invisioncic.com/y282845/emoticons/eyebrow.gif.fe2c18d8720fe8c7eaed347b21ea05a5.gif but, because it has stored voltage already, the cap can draw voltage from the battery, lets say 100 more times, before making the alternator send more current to the battery, then your amp being directly connected to the battery can before making the alternator send more current for charging the battery. The cap helps.
WB
Your severe lack of understanding in the physics behind electrical circuits makes me want to throw up.
A capacitor, in every physical form, has the same mechanics. It holds charges to be released VERY VERY VERY VERY VERY VERY VERY VERY, etc. rapidly. I'm not talking about a one second discharge. I'm talking about a millisecond discharge. I've done the math, a one farad cap can discharge I believe 400 watts, or something like that. Now, that's pretty good, but, what you must know is that the alternator is ALWAYS charging.
But here's a science project for you to do.
PRIOR KNOWLEDGE:
Your car needs electricity to run. To run both the spark plugs, and the ECU (unless you have an older car with a carburetor.) With this knowledge, we go onto the test:
TEST:
Start up your car, disconnect the battery from the circuit.
FINAL CONCLUSION:
THE CAR STILL RUNS!
This is because the alternator is giving a steady stream of power. In all technicality, your battery should not be needed for the actually running of your car. It's there to start your car. Period. That's what it was designed to do, and that's what it DOES do. But when you add things onto your car, aftermarket things, such as lights, and gizmos, and speakers, the battery becomes necessary.
What a battery actually does in the car audio world, is fill in when the alternator cannot supply the sufficient current.
"WOAH WOAH WOAH! WAIT SCOTT! Isn't that what CAPACITORS DO?! Now I'm just all confused!"
Capacitors have a much faster discharge rate (versus batteries). Now, I'll reiterate what I've said before. CAPACITORS HAVE AN EXTREMELY FAST DISCHARGE RATE!
So, if your system is using 50 amperes, and suddenly, it needs 150 for a millisecond. Then, yes, a capacitor will help. But if your system needs 70, and your car can only supply 50, then a capacitor won't do beans. A battery will help, but it won't fix it.
All of these things are little bandaids.
Bottom line is: if your lights are dimming, then your amp isn't getting enough current. Get a bigger alternator, or do the big 3. A capacitor AND a battery is just covering.
The small amount a capacitor helps, it hurts just as much. Because as the amplifier is trying to draw current from the alternator, so is the capacitor.