I didn't know. So I went onto the Facebook RV Solar page and asked the experts and as usual, the answer is "It depends". It depends on how good a solar controller I have - mine is a lower end Pulse Width Modulated model and if it is programmable - no it is not. The consensus from the experts was that I was getting very little (if any) charging from the panels while I was plugged in. Well, that's not why I invested several hundred dollars into the 325 watt system of three panels, four batteries and a controller.
I was advised to turn off the breaker powering the converter. This would turn the charging duties over to the solar converter while still leaving the rig plugged in and the wall outlets powered. The best of both worlds.
I opened up the breaker panel and there it was, breaker #2 clearly labeled, "Converter". I turned it off and watched my battery voltage drop from 13.7 volts to 13.6 as the solar accepted the load. A few minutes it was at 13.8! It was working even in the overcast condition we then had. Now I just have to monitor the voltage to make sure it keeps up.
Thursday morning EDIT: This morning under a bright sky it was equalizing at 14.8 volts! I am a happy camper!!
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