I have a laptop which, when put to sleep, sometimes enters a state of limbo, from which it can be neither turned off nor on, and the only solution is to disconnect the battery, reattach it, and turn it back on. When I disconnect the battery, all the power vanishes, and I have to recharge it before I can use the laptop. The question is, why is this the case? The energy must go somewhere, and I haven't noticed my laptop ever suddenly get extremely hot when I take out the battery. So what happens to the electricity in the battery when I remove it?
Where does power in the laptop go when I disconnect the battery?
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Your battery is going bad (probably).
The battery is not suddenly losing all of its stored energy when you pop it out of the laptop. There is no mechanism for that to happen without getting extremely hot and probably exploding from the outrush of current. It has exactly the same amount of stored energy in it before and after you disconnect it.
Here's the sequence that I suspect is happening:
You start off at the beginning of the day with a fully charged battery. The battery is old and is not able to hold as much charge as it used to, but it's enough to power the laptop for now.
Over the course of the day, you drain energy from the battery while using the laptop.
You put the laptop to sleep and let it sit. But since you've been using for a little while, it has very little energy left. Its internal resistance is very high (hallmark of an old, used battery).
The laptop continues to drain a small amount of current from the battery while its in sleep mode, causing the battery to drop further into the danger zone.
You come back and try to wake the computer back up. The laptop attempts to spring to life and draw a bunch of current from the battery. In the battery's youthful days, this was no problem. It would have had plenty of charge capacity left and its internal resistance was lower. But now it can't handle the sudden current surge when its nearly depleted. Its voltage drops and its unable to power the laptop. However, it is able to maintain the small trickle of power to keep the laptop in sleep mode.
You take the battery out to cut power to the laptop. You put the battery back in and try to turn it on... but you're only repeating the same thing as before. You won't be able to turn the laptop back on using its battery until its been fully charged again.
My guess is the power monitoring circuitry of the laptop sees the battery voltage drop when you're trying to wake it back up and prevents the motherboard and peripherals from booting back up. This prevents the electronics from experiencing a bad brown-out, but it prevents you from waking the laptop out of sleep mode.