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I have a couple of 12v batteries that I'd like to use to power a cooling apparatus while camping for several days.
I also have a 15W solar panel I'd like to use to top-off the battery.
Can I use the battery while it is charging? Or would I have to disconnect the solar panel prior to using the battery?
Alternatively, I could charge 1 battery while using the other, and simply swap them out - is this preferable?
While it is true that you can't actually charge and discharge a battery simultaneously, it is quite common to have a charging source, a battery, and a load, all connected in parallel so it looks like you are charging and discharging simultaneously.
If the charging source can deliver more current than the load requires, then the excess current will be used to charge the battery. If the charging source delivers less current than the load required, then the battery will supply the extra current needed. This switching between charging and discharging will happen automagically as the charging source and load vary.
If by "use the battery" you mean "can the battery be in the circuit?" then yes.
If by "use the battery" you mean "draw power from the battery while charging it?" then no. Charging is, by definition, putting power into the battery. This is the opposite of drawing power from it. You can't do both, by definition.
Under normal operation, where the battery is powering a load, conventional current flows inside the battery from (-) to (+), through the load, and back to the battery. If something else (like your solar panel) can apply a voltage higher than the battery, then the battery becomes "the load", and current will flow through it in the other direction, reversing the redox reaction inside it, storing electric energy from the solar panel as chemical energy in the battery.
Of course, you have to make sure this current is within the operating parameters of the battery. If you charge a battery too fast, or too much, with those limits depending on the particular battery and specified in the datasheet, it will be damaged, destroyed, explode, or otherwise bad things will happen. Don't do that.
You also want to make sure that when there is not enough sun on the solar panel, and thus its voltage is lower than the battery, that the solar panel doesn't become the load, with the battery driving a (potentially very large and destructive) current through the panel. Usually this accomplished with a series diode.
There are, of course, no shortage of commercial products designed to charge batteries with solar panels. It's basically the most common thing to do with solar panels. Such a device will take care of monitoring the charge on the batteries, being sure to not damage them, preventing reverse current, etc. Some are sophisticated enough to adjust the operating point of the panels for maximum efficiency and other such neat stuff.
If you operate a laptop while its battery charger is connected, then you are familiar with the concept you ask about... Yes, you can. Answer 2 and the aforementioned laptop powering are JUST what you propose. Just be sure not to cause a deep discharge... some batteries will not recover. NiCads can even reverse polarity.
