I have a sealed lead acid 12v 24Ah Battery but Can I charge it with a 12v 60w of Power Supply adaptor?

To a degree. But you must be careful. Chargers that are designed to be chargers will charge a battery to 13.6 volts. That's the float voltage for sealed lead acid batteries. I know this because I'm a Power Generation / Distribution / Power Management engineer. Been that for nearly 30 years.

The thing about using a 12 volt supply is they are not regulated. RMS voltages mean Root Means Squared, or the effective voltage of an AC sign wave. Before you try charging the battery try charging a capacitor that is rated at least for 18 volts. Using a DVM (Digital Volt Meter), measure the charge. You will discover that an RMS signal has substantially higher voltage than the RMS rating.

What will happen to the battery is you will over charge it. Which will over heat it and cause the electrolyte to boil off it's moisture, leaving it dry and useless. The battery will be harmed. Even if you charge it then use it and it seems to be fine, you've done damage. A second charging and you damage it further. Enough charge cycles and the battery will become useless. And I don't mean in the next few years.

Put the battery on this charger and forget about it for a few days and when you get back the battery will be shot. GUARANTEED! I've messed enough with batteries in my career, and I've seen exactly what I'm warning you about. If you're looking to save a few bucks then go out and buy a real battery charger. One that's designed to not over charge a battery.

That alone is the biggest reason why you are not supposed to charge batteries of differing types on chargers that are designed for a specific purpose. Your only other alternative is to build a regulator circuit that can manage whatever charging current you use. Your 12 vdc 60 w adaptor is capable of putting out 0.2 amps (or 200 milliamps). That's not much to charge a 24 Ah battery. In theory it would take 120 hours to charge the battery to full capacity. In other words, FIVE days.

So, practically, no you probably wouldn't want to use this power supply as a charger. But if you do, and you leave it on for a week or two - or all the time as a reserve power supply, you will destroy the battery.

Your project is impractical AND ill-advised.

Best of luck with your project.

'')

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I have a sealed lead acid 12v 24Ah Battery but Can I charge it with a 12v 60w of Power Supply adaptor?

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A 12V charging system will put out anywhere between 13.8V and about 18V DC. Direct current is needed for charging. Depending on how big your "smallish" battery is will determine how long and if it can charge your battery. A 500mA supply is .5 A . So for a car sized battery this would only amount to a trickle or maintenance charge, and could be left on almost indefinitely. As the battery size gets smaller you run the risk of an over-charge rate and over heating. For a garden tractor size bat. I would recommend, say, 24hr charge then check voltage of the bat. For smaller sized bats. try 10-16 hr charges and check voltage and the temp of the bat. If it feels very warm after only a short period 1-2 hrs. you are charging at too high a rate,and either need a smaller charging unit or possibly charge more than one bat. at a time, to handle the extra amperage.

12v 24ah Battery