Q*: “When a laptop is plugged in, how does the battery get charged and the laptop get powered simultaneously?”
A: There are, in effect, two parallel circuits in most laptops; and the laptop’s OEM charger is sized to provide enough power for both.
When your laptop is turned on and is plugged into a wall socket a, some of the charger/power supply’s output will be shunted to the battery for recharging, while the rest is independently available for direct use by the PC’s circuitry. The latter’s power usually doesn’t have to “go through” the battery first, when there’s external power available.
You can prove this to yourself. Remove your laptop’s battery, then plug the laptop normally to a wall socket: Even with no battery installed, most laptops will start and run just fine.
(I had a related question on laptop power just yesterday: see this.)
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