I have two VRLA batteries, 2Ah and 7.2Ah in capacity. Both are 12v. What would happen if I connect them in parallel when they are charged to the same voltage? can I use them to power a 10w LED? what will be the effect on the two batteries in parallel when drawing current from them? (These are to be used with a 10W solar panel)
i'm not an expert but...
"Most battery chemistries lend themselves to series and parallel connection. It is important to use the same battery type with equal voltage and capacity (Ah) and never to mix different makes and sizes. A weaker cell would cause an imbalance. This is especially critical in a series configuration because a battery is only as strong as the weakest link in the chain...
A weak cell may not fail immediately but will get exhausted more quickly than the strong ones when on a load. On charge, the low cell fills up before the strong ones because there is less to fill and it remains in over-charge longer than the others. On discharge, the weak cell empties first and gets hammered by the stronger"
you need only 1ah to run a 10watt load on a 12v battery. your 2ah will last 2 hours from a full charge if you use only that. if you need it to run longer then the 7.2AH would last most of the night.
Be careful when you say charging batteries to the same voltage, as you can see in the picture below, a lot of batteries have a pretty consistent voltage output even though the state of charge is definitely decreasing, because of this voltage is usually a really bad way to compare charge.
Better way is to charge and deplete batteries, measure the actual energy going out and determining it in such a way. Also the changes in batch, build and all will definitely cause one of the batteries to charge/discharge more quickly then the other even if they were identical battery models.
From your question I understand you want to use the batteries as energy buffer/storage for your solar panels and power a LED of those, The easiest solution would be to just use 7.2Ah battery by itself.