You do not need to pull a battery cable to check the alt. All you have to do if you can get the motor running is hold a piece of metal by the back of the alt. If the alt. is working, it creates a magnetic field and will attract the metal object. (note) you have to use a piece of metal that a magnet will stick to.
All of these things test certain aspects of the charging system but not the whole picture. Most chain parts stores will test these things for free so this is the easiest. The battery must be at full charge to be tested though (which they will do but takes a while.)
That's true but if you can't get it to the parts store, my way is a good way to find out if you need a battery or alternator really fast
regulator? I've got a problem with overcharging, anybody else have this happen? The battery boils out over time, and I'm told it's the regulator, but I replaced it, it still happens. Is your battery dry (dead cell?) If so, be careful charging, the battery could be full of hydrogen, and if it is dry or low, use distilled water to top it off, then try it out. The water will displace the gas, so less chance of an explosion. You don't want to see that happen, trust me.
