Should you remove the battery from your laptop when the charger is pluged in?

Well the battery will not charge if it's not in the computer while the power supply cable is inserted into the laptop. It used to be you had to remove the battery when it was fully charged, but modern computers can detect a full charge on the battery and will not overcharge the system.

It is perfectly save to leave a battery in the laptop while the power is being provided by the wall outlet or car outlet.