Amps = Watts/Volts. So figuring for (approx) 80% efficiency of the amplifier, you can figure on most amplifiers drawing about 85-90 amps per 1000 watts of output. Even many 'daily driver' systems these days utilize a few thousand watts.
I dont know why your cap discharged itself, it shouldn't. Does the cap have a voltage display? That would drain the cap fairly rapidly once the cap was disconnected from the batt/alt.
External caps are largely misused by the car audio community. And the car audio industry feeds off the basic misunderstanding, to make a buck. A cap, even a relatively large one like a 1farad or more, will discharge very rapidly (given the potential in system voltage drop). Small storage capacity, very rapid discharge rate. So with a car whose stereo grossly overpowers the charging system, the cap will dimply discharge down to the system voltage drop, and remain there until the charging system catches back up and voltage rises again. Since the cap's capacity is so small, and discharge rate is so high, it only provides a benefit to the system, in the form of being a power source, for a fraction of a second. This is why I say most car audio enthusiasts using a cap are using it for the wrong reason, as some sort of bandaide for an over taxed charging system. And the industry is making a buck off of this misconception, they market them as a charging system crutch.
The first person to use an external cap in car audio was Richard Clark. If you dont know who he is, he's a well known engineer, audiophile, car audio SQ previous world title holder, etc. Even Clark agrees that a cap will not help a weak charging system. He placed a cap (an array of smaller ones actually) before his amplifier(s) in his competition SQ car for SQ purposes, not because his alt/batt was insufficient. Richard Clark has very vocal for many years now about his views on the industry taking advantage of his idea, and twisting it into something it never was, to increase their profits.
Caps *can* benefit an audio system in the form of SQ because that rapid discharge rate can help supply an amplifier with current it needs in a more dynamic way than a tradition battery. In other words, as a bass note hits, the cap can discharge power very rapidly to catch that increase in current draw much faster than the batt. This very quick amount of supply power the cap provides will never be any real solution to keeping your battery from going dead (a bandaide for a weak alt), but it can help your charging system be more dynamic in providing the continuously varying power the stereo needs.
Now before anyone runs out and buys a cap because I told them it would improve their SQ, keep some things in mind. IN a system that has a sufficient sized alt, your system voltage may never drop, avoiding the cap from ever really discharging, thereby giving no benefit to the circuit. This is rare, as even 'H.O. alts' usually see some power draw spikes that will force it drop its voltage output, but its certainly possible.
Next point to remember, with a large enough system, by the time you array enough caps to get sufficient capacitance to make any real difference, you've probably added so much resistance to the circuit (caps do possess their own internal resistance) that you've outweighed any benefit you would see from the caps.
Next point, it would take a 'golder ear' to hear any noticeable difference in sound quality a cap would most likely provide, since it would be capable of discharging in fractions of a second. Im confident even Richard Clark would admit he mostly added those caps to his SQ car, all those years ago, simply for 'visual SQ' to appeal to the judges. Judging SQ is, of course, subjective. If a judge sees some fancy new gizmo under the hood that is suppose to make the stereo sound better, a psychosomatic episode tends to occur where that judge thinks it sounds better. This is a common tactic used by SQ competitors clean wiring tends to make a system 'sound' better.
Next point to remember, your amplifier already has an array of 'stiffening capacitors' in its input stage. So, in essence, when you go out and buy an external cap for your amplifier, you are telling yourself that either you know more about amplifier designs and the necessary input capacitance than the person who designed your amplifier, or you are buying it because you regard the amp's quality as not worthy of trusting that it was designed/implemented/built well.Read what Im saying one more time, slowly, and think about what it means... your amplifier already has stiffen caps
built in.
Last point, for an insufficient charging system, a cap will make no real improvement. Some people experience less headlight dimming from this, which is possible, but ultimately all power must come from the alt. If the alt doesn't produce more current than you are drawing, the inevitable is a dead battery. There are many factors to consider though, such as how often you run your engine without the stereo being on, how loud you tend to listen to your stereo, and even what type of music you listen to can contribute.
An extra battery helps by adding to the storage capacity in the circuit. When the music is quiet (or the stereo is off altogether), and there is a surplus of power from the alt, it charges the battery. When current demand raises above the ability of the alt, that stored energy in the batt(s) is released to pick up the slack, until the demand decreases to a point that the alt is sufficient again. The more batts you have, the greater time can occur between sufficient alt and insufficient alt periods. But, even a large storage bank of batts requires a surplus of energy from the alt once in a while, or it will eventually go dead as well. So again an extra batt is a poor bandaide for an insufficient alternator. A second batt, presumably in the trunk, also provides a small benefit of having a power nearer to the amplifier(s), to minimize resistance in the supply circuit for those rapid transient spikes.
Music is transient, so the stereo's power demand is also transient (going up and down). Is for this reason that you have to look at power draw from your stereo as an average over time. Most people look at it as an instantaneous snapshot in time (my amplifier draws X amount of current, my alt provides Y amount of current), this type of thinking leads to inherently flawed logic and conclusions. One of which being that external caps will help a weak charging system.
There's tons of information on caps out there on the web. If you want to read from an expert, go to Richard Clark's forum over on carstereo.org (iirc) and read it straight from the horse's mouth. He invented the use of external caps in car audio, he's an electrical engineer, and he doesn't pull any punches to excuse an industry that all but lies to its customers to sell them a product they rarely see any benefit from what so ever.
A good website for basic car audio information is bcae1.com. The page talking about caps is here:
Capacitor
Hope that answered all your questions.