I am looking to add charge indicator circuit which detects battery level and disconnects.
As long as the voltage is set precisely, there is no need to disconnect - a lead-acid battery can be left on float charge forever. The charger needs to be current limited though, to prevent it charging too fast.
The charge happens in two stages; first the voltage increases until it reaches the set value, then the current gradually falls off until it gets down to the trickle charge level - probably somewhere between 20 - 50mA for that battery.
When the battery voltage reaches maximum, it's only somewhere between a third and half full charge - you must monitor the current as well, to work out the state of charge.
(If you look at any old, non-microprocessor type battery charger they have an ammeter not a voltmeter, as you know the battery is charged when the current gets to a low value).
eg.
From my late father’s garage.
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Input 110-120 Vot AC 50-60 cycles.
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If you try to copy some online supposed battery charge controls that use voltage detection only, it will
not work properly at all. Never assume online or youtube posted circuits are correct - there are more incorrect than there are working!
The battery you have is only 1AH capacity, so the maximum charge current is probably around a 250mA.
Too much current will wreck the battery very quickly.
The capacitor value depends on the transformer. The voltage should be at least double the transformer secondary voltage; higher is Ok.
The capacitor value depends on the load current. I'd probably use 4700uF as a rough guess value.