Problem with Charging system!

I noticed that the needle goes to about 11-12 volt during stop or 900 RPM.
the weather these days very cold about ~ 4 c. night.
I changed my alternator before year with new one!
when the engine runing in normal codition say above 1000 RPM , the voltage goes and stay ~ 14 V.

q: is it possible IF the battery is weak ,even with engine runing the voltage can be drop as my situation??!
where is the problem you think guys?

GUess why i post this thread in Parts wanted??
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I WAS SMOKING!