Is it OK to use an iPhone 4 that is fully charged while keeping it plugged to wall outlet?
I am worried about stressing battery too much since it is charging and discharging at the same time.
Any issues here?
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None whatsoever unless you somehow drop the phone since it's attached to a cord.
The charging system on iOS devices is adaptive and only engages when the battery needs charging current. It's smart and slows down the charge appropriately whether you are using the device or not.
Put another way, the device only asks for enough power to run itself and charge if needed from the wall. The wall doesn't send too much power so there's no risk of overcharging.
TL;DR - Perfectly safe.
The iphone doesn't accurately display it's current charge level with the on screen indicator. If you turn if on (it's in Settings, but off by default) the available battery range is the standard 0-100%. But when it hit's 0%, it still has enough juice to safely close all your apps and save their state for future use. You can test this by having a text half written as your phone dies. Charge the phone u p, and hey presto, your half written text will be there to the letter, because it didn't just pull the power and turn off, it gracefully closed all the apps.
Likewise, when it hits 100%, it doesn't actually stop there, it continues charging even further. I'm not sure for the phone, but I believe that on an iPad 3 it will charge to the equivalent of something like 107%. Why? Well, leaving a battery fully charged without using it, is bad for it's health. Also depleting a small amount of charge (say 2-3% and then recharging is also not ideal. That's why if you have a Mac and you charge it fully, then use a bit so it drops to 97%, and then put it on charge again, it won't actually charge it any further, and will stay on 97% until it drops lower than that, at which point it decides it has safely depleted enough to make it worth charging again. The iPhone does something very similar, but is more clever about it. So it will say 100% before it has actually reached it's charge limit, and from that point on until you start to use sufficient battery, it will charge it to 107% (equivalent, roughly), then use battery until it drops back to %100, then charge to 107% etc etc and so on, so it never just sits there at full charge. You have have noticed that occasionally when at 100%, it will take a long time to hit 99%, this is dependant on whereabouts in the "overcharge" cycle it is in.