Normally your battery warning light comes on to warn you that it is not getting sufficient charge. If that does not come on then its either a faulty battery or the light does not work as well.
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It is possible that a bad diode in the alternator will prevent it from delivering full rated current, while still keeping the light off. The general way to tell is to be sensitive to the way the engine cranks. If it is cranking slow, then you have a starter and/or alternator and/or battery problem. Unfortunately, one can cause the other to fail, so you definitely need a good mechanic to check out everything when something is replaced.
As an example of a worst case scenario, the bad diode prevents the battery from being fully recharged after starting the engine. The battery voltage falls. This causes the starter to pull more current on subsequent starts. It begins to overheat. Maybe a winding shorts out and the Q factor goes to pot. One day, the starter pulls so much current that it buckles the plates in the battery. Now you have a bad alternator, a bad starter, and a bad battery. Replacing one, without carefully checking the other two, could well cause the new component to fail again.
Perhaps thids might help... http://wiki.answers.com/Q/How_do_you_tell_if_the_battery_or_the_alternator_is_bad
There are generally two signs that the alternator is going bad. First is the noise. A new noise will begin to be heard. Something like a whining when the car is accelerating. Second is the smell. You may smell burning from the engine department.
Take the belt off and spin the alternator by hand. If you hear a grinding noise, like sand rubbing on metal, its probably going bad. Also try to wiggle the pulley up/down/left/right. If it wiggles, the bearings are going bad. Of coarse you can always wait until they get so bad they shatter and the alternator wont spin at all, like i did. :(
When your battery does not get charge.
If bearings go bad they will "squeal"
There are a few reasons why your alternator might keep going bad such as rusty latches under the car. You may also have leaks, dents, or parts that need to be replaced on the vehicle that are effecting your alternator.
How to Tell If Your Car Alternator Is Bad Check related link below…
Normally this is the bearings going bad.
There are several signs that an alternator is going bad. A few signs are dim lights, smell, warning lights, and a dead battery.
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Alternator is going out? battery is going bad?
A bad alternator will make whats called a whirring noise. It could also make a low growl. This is just the bearings going bad. If your alternator is not supplying any power, it has nothing to do with noise typically.