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I know how a laptop battery becomes charged, however, I am not so sure how the power is maintained when when the battery has been charged to the maximum.

I am unsure whether the laptop would switch to take power solely from the power supply or would the battery be replenished as soon as it is used up.

Can someone who is knowledgeably of how this works explain to me how exactly does a laptop maintain power once the battery has been fully charged?

Is this true for ANY device?

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    \$\begingroup\$ Even if a device switches to powering off of the adapter when the battery is full (so that the battery is not used), the battery will still slowly self-discharge. Therefore, there must still be circuitry to monitor the battery and start charging again. Otherwise, if you used your laptop on AC for a year and then disconnected the AC, the battery would already be low or dead. \$\endgroup\$ – DoxyLover Dec 23 '14 at 23:41
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That basically depends on the manufacturer.

I've had one laptop that would indeed fully charge the battery, then switch to battery power until it dropped to 95%, then restart charging. The battery died within six months, and I haven't bought from that vendor since.

Typically, the battery is disconnected when fully charged, and then monitored for self-discharge, and after dropping to a certain level, it is again fully charged. This level is chosen as a trade-off between limiting the amount of charging cycles and risking a less than full charge. Again, different vendors choose different values here, between 98% and 85%.

As an extension, some controllers also differentiate between continuous power with the battery level dropping below a threshold, and being plugged in while the battery is below the threshold (many devices are unplugged for short times while moving to another room), look at current power usage (if the computer is turned off, the supply may be unplugged soon), number of batteries installed, past charging behavior, ...

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The Laptop/Computer simply stores away most of its leftover power in Capacitors, and once it gets to 100% it activates a function, and uses the power in the capacitors. This function is available in pretty much, every device. Sorry for the short-answer, I'm quite new to this kind of stuff.

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    \$\begingroup\$ Capacitors store insignificant amounts of energy, compared to the batteries. They're really just there to reduce the impedance of the power distribution networks of the computer in order to minimize the effects of noise. You should consider deleting this answer until you can come up with something better. \$\endgroup\$ – Dave Tweed Dec 24 '14 at 16:31

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