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It would depend on what load you applied to the Inverter ,not the wattage of the inverter itself.Batteries are best when matched size and power and Age! Simply connect POS to POS and Neg to Neg. Connect the inverter to POS on one battery and Neg on the other. 2000W is quite a load on even two batteries. I have Three but only use 1500W Pure Sine inverter.
The power of a solar panel mostly depends on its area. So you could measure the panel size, and compare it with the sizes of panels sold online, to give you a ballpark figure for the panels. If you could read the panel label that would be better, but it's probably inaccessible.At the moment I have 2 solar panels not sure of size of panels 1 2000watts inverter and 1 12v battery but would like to fit another battery but not sure how
I know what you mean, just trying to point out the limitations.It would depend on what load you applied to the Inverter ,not the wattage of the inverter itself.