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The only way to charge a battery from AC is to first convert the AC to DC. The DC should also be slightly higher voltage than the nominal voltage of the battery. For example we can charge a 12.6 volt car battery with a small battery charger that has a transformer to convert the AC house power down to a lower AC voltage and then we use Diodes that change the AC into DC. The DC voltage that comes out of the charger is usually about 13.6 Volts for a car battery. Some batteries like lithium batteries are much more complicated to charge and require more complex circuitry with some intelligence. You used the term "inverter" which usually refers to a circuit that takes the DC power of a battery and converts it into AC power so that household appliances can be run on a battery. If this doesn't answer your question ask me a followup question.
That is really nice answer, I was also looking for this issue for my project. Thanks for the help.
Hello, i am brian, i was wondering if there was any way to charge a DC battery using ac and not an inverter. because i cannot afford inverters that actually last long enough to be worth what i paid. so i want to charge dc batteries without having an inverter. and i was told most batteries run off of dc so i could just use a charger for those but i wanted to ask the public and see if it (CAN) be done