Cap/RPM Problem

I got my amp and sub installed about 2 weeks ago. I have an audiobahn aw1200q and a jbl 600.1. I installed my lightning audio digital 1 farad cap about a week ago. When my car is on it shows 14-14.1 but when the car is off it shows 13.5 or so and will turn off shortly after. Is it suppose to turn off? my friend's cap is always on and i was jsut wondering if it was different due to brand. Also when im at idle and i have the bass up my idle gets rough. It can fluctuate from 900 rpms down to about 500 with the bass hits. My lights dont dim at all, so does that mean it is taking the power from my ignition? Does this mean it is time to upgrade my alternator? How bad is this? thakns for any help.

The cap is fine it is supposed to turn off when there is no current draw and your friends should to. As far as the rpm's fluctuating .Fosgate has a good article that you should read Why do engine RPM's drop when bass hits in my car?Hope this info helps.