If your Beetle has a generator (dynamo), it's electrical output is 30 amps (360 watts). If it has an alternator (easily fitted) it is probably a 60 amp (500 watt) unit, although there are higher capacity units around.
The VW alternator is also designed to run at slightly lower rpm than most other alternators, as the speed is set by the pulley dimensions to suit the fan requirements. Most alternators have a smaller pulley for higher speeds, and this is why alternators will charge at idle, where generators won't (your lights will get brighter as you tap the throttle).
You can measure the voltage at the battery -- and thus make sure a charging current is going to the battery from the alternator/generator. Start the engine and read the voltage across the battery terminals with your Volt/Ohm Meter (set at 15 volts). As the engine speeds up, the voltage should increase to about 14.2-14.5 volts. If it does, then the generator/alterator is working properly and charging the battery as it should. At idle the voltage across the battery terminals should be somewhere between the 12 and 14 volts. Current is harder to measure as you are talking about a LOT, although one of those simple amp meters in the line (main red lead from back to the fuse block) might tell you the story.
The alternator doesn't charge any "better" than the generator, but it will start charging at lower revs (even though the VW generator is described as an "early cut-in" design), and can produce more amps for roughly the same physical size. The other main advantage of the alternator is that it has 'slip rings' for the brushes, which are smooth rings around the shaft - making for low wear on the brushes and low radio interferance compared to the segmented commutator on generators.
The alternator with it's 50-60 amps also allows for more electrical gear, like the boost fan in the dash. With all my lights etc. on I have only about 120 watts spare with my generator, which is fine if you don't want a big stereo and spot lights (I don't). I used to run with spot lights (2 x 55 watt), without the battery going flat, but I found that the H4 55/60 Halogen headlights I have are just fine for night driving (we still use the globe and reflector headlights, not the sealed beamsyou've got in the US).
Dave found that an alternator, even a new one, will hold a charge in a battery but will not establish one. The circuitry of an alternator is such that it needs a good voltage from the battery to feed the alternator windings so that the magnetic field is established inside, before the spinning rotor will make any voltage - i.e., it needs a good "feed-back" voltage. This has something to do with the fact that the alternator has diodes to rectify the alternating current, and so you need 12 or more volts from the start to get these to feed power back to the battery.
A generator needs a starter current too, but it's much less critical, and a half-dead battery will provide enough to get the charge current started. Then this charge current will feedback through the battery to the field windings (the stationary windings inside the shell) to build it up to the 14 volts needed to start charging the battery correctly. Both the battery and generator are direct current, so they are "on line" to each other even when the battery is half dead. The alternator only comes "on line" to the battery after the voltage reaches 12+ volts.
Alternators use current regulation instead of voltage regulation, and most alternators (except the 'first' VW ones) have the regulator built in to the back of the alternator, so it gets cooled from the little fan behind the pulley. They usually have a "plate" about 2x1 inch on the back which has both the diodes (turns the alternating current into direct current) and regulator behind it.
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