Ok, it seems like your computer is set to run on a lower power setting to preserve battery when the power is unplugged, therefore the screen dims in brightness. All laptops are like that by default, however this can be changed. But be advised, this will consume more battery power if you wish for the screen to stay just as bright when the power cable is unplugged.
Follow these steps...
Start > Control Panel > (If your using category view, click on Performance & Maintenance > Power Options) (If Classic > Power Options).
And from there you can change the setting!
Let me know if this helped
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