YES, leaving a fully-charged device on its charger will kill your battery, but it's not from overcharging....
NiCd and NiMH batteries developed memory effects that required you to fully charge/fully discharge your battery to ensure long life.....
Lithium Ion batteries, like yours, do not require you to fully cycle your battery in this manner, BUT, and this is a big BUT, lithium ion batteries have a very finite NUMBER of charging cycles, that is to say, the battery may only be charged/discharged 500 times (I just chose a random, arbitrary number there).....once you've reached that point the battery's performance will decrease until you eventually get to where you're at now.
What does this have to do with overcharging? Well, it's not "overcharging" per se - as others have noted there is circuitry in your device to prevent overcharging - the problem is that your device will:
1. charge until it's 100%,
2. the protective circuitry will interrupt the charging to protect against overload,
3. the battery will slowly drain as power is being consumed by the device,
4. the circuitry, sensing the battery as being at something less than 100%, say 99% (or whatever threshold the designers stipulated), will now allow the charger to do its thing again,
5. the circuitry stops the charge when it gets to 100%...
voila! you just burned-up and entire charging cycle going from 100% to 99% back to 100%....using my arbitrary 500 cycle life-span example, you now have 499 charges left until your battery turns to garbage......
Now, think about how many times per night/day your device is doing that...how many cycles are you using in an average day, just by leaving it on the charger overnight? You could be using up 5,6,7 (or more)cycles per night...
With cell phones you can replace the battery pretty easily and cheaply; with most rechargeable devices, however, you may have to send it to the manufacturer to be replaced or it may not be replaceable at all! (ask about SanDisk)
Personally, I hold off charging my devices until they're quite low and in real need of a charge; this goes doubly for my iPod, since the battery is not user-replaceable. The ONLY devices I've had problems with were those with which I failed to heed my own advice.
(incidentally - many laptops have an adjustable battery management feature that allows you to lower the threshold at which the charger kicks-in, just for this very purpose)
So YES, leaving your device plugged into a charger when it doesn't need charging will shorten the life of your battery.
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