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In my Project I used below battery and a battery back SMPS.

Battery Type:- Sealed Lead acid , Volt:- 12V, Ah:-7AH Charge parameters:- Constant voltage charge with voltage regulation Standby use 13.6V-13.8V Cycle use 14.1V-14.4V Max initial current 1.4A

SMPS Input 85Vac to 264Vac , 50Hz Ouput :- 13.8V DC Below image from SMPS datasheet enter image description here

I read the SMPS datasheet , but there is no information of charging and discharging of battery timing.

Load I have connected a load of 20W at +v and -V terminal.

Q 1) I setup everything, Connected the battery, put a multi-meter across battery terminal, voltage on display slowly slowly increasing. At what level I know that my battery is fully charged and I should disconnected it to being overcharged.

Q 2) About Battery Backup time.

 a) If we use formula  Tbck= (Vout* AH)/(op Watt) , i got 4.2hrs. Is it    Right calculation

 b) If I use other formula with Battery spec (see attached image)

enter image description here

Consider 3HR rating of 5.2AH. Current= 5.2AH/3HR = 1.73A current it can supply till 3 Hrs. ( right ??) so after 3 Hrs how much voltage of battery will be
0 volt or 10.5V. Since my SMPS cut the battery if its lower than 10.5V.

Q 3) Charging time of battery

Since no information given in SMPS datasheet about charging current or else, can not figure out about charging time of battery. a) Battery is constant voltage regulation charge type and SMPS is charging the battery with 13.8V, then any method to calculate the charging time of battery.

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You're confused about charging times while you should not be. It is actually quite simple because you're using a SLA battery. You can charge such a battery simply until it reaches 13.8 V. This can be done simply by connecting it to a 13.8 V voltage source, which is your SMPS.

Do make sure there is some form of current limiting in place so that the current does not get out too large when the battery is empty and 11 V for example. I expect your SMPS to have proper current limiting but if it current limits at a high current, check that the battery is allowed to be charged with such a current. If not you may want to add a power resistor between the SMPS and the battery to limit the current.

When the battery is full it's voltage will be around 13.8 V and charging will stop automatically because battery and source will be 13.8 V. There is no need to keep track of charging time. Most Uninterruptible power supplies have SLA batteries and they charge them this way because it is simple and effective.

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