Is it OK to charge a 12V sealed lead acid battery just by connecting it to a 13.8V power supply?

I guess this is called float charging?

I don't care about how fast the battery charges - I just want to leave 13.8V connected constantly across it, for an indefinite period of time.

billrussell422012-07-08T13:22:59Z

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could be, but the correct float voltage varies with temperature, and with exact battery construction, so contact the manufacturer to get the correct float voltage for various temperatures.

It might be easier to just provide a small current source, say 2 amp for a large lead acid battery. You can approximate this with a voltage source and series resistor. The resistor will need to be a high power type, as the current will be high when the battery is discharged.

?2012-07-08T19:43:36Z

Maybe, but I would recommend a charger that is designed to reduce the current to provide a trickle charge, when the battery is fully charged.