quick question about alternator

[pbanders]

Have you tried charging the battery on a charger? Don't assume that just driving around is getting you to full charge. When a battery is fully charged, after you let it sit for a few hours to dissapate the surface charge, you should read a voltage of 12.75 V. Anything lower than that (e.g. even 12.6 V) means the battery isn't fully charged,

If your system voltage is 13.8 V, your alternator is working. If you start with a fully charged battery and it's not staying at 12.75 V after you drive the car, the battery needs replacement.

[gschotland]

Did you test your alternator output with maximum load? Put your headlights on, heater fan on high, stereo on, and anything else you have that pulls juice, then see what the output is. With this load it may no longer be in the normal range, indicating an alternator problem.

[Steve Tinker]

And when (if) you charge your battery with an external charger, you need to disconnect the battery leads from the car & leave it being charged for at least 12 hours......
Then do your voltage check.