A couple more pictures, taken when back in the office today, running off the Dell OEM 45W Mains Adapter / Charger.
At full charge current, Display is Dim, noise is absent.
Image may be NSFW.
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In this case I guess it's hard to tell but believe me, with the adapter unplugged, the display goes Bright! No noise though.
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A couple of other points. The system correctly reports the capacity of the Power Adapter that is connected, but for some unknown reason, sometimes it switches to Low Charge Current mode. I haven't correlated that to anything yet, except that when it does, the noise happens.
However, it happens more when the unit is cold, and more easily when running off the Car Adapter. Sometimes, messages appear (in Diagnostic Test mode), saying "Warning: Charger is not detected, please attach the charger now" even though the charger is connected and running.
To get the machine into Low Charge Current / Noise Generator mode, it's usually a matter of plugging and unplugging the power adapter when the machine is "in the mood". Sometimes, it is ok, sometimes, it switches to Low Charge Current, and starts making the noise. It seems to be something to do with whatever system is detecting the power adapter, the temperature and the battery charge state (%age of full charge), and then setting the charge rate. Sometimes it happens when you plug the cord into the side of the laptop, other times, it happens when you turn the adapter off and on at the wall switch.
Like a previous poster, I have listened carefully to the noise, and agree that it's coming from under the keyboard in the vicinity of the Backspace key. In my view, it's pretty much under the +/= key.
And it's happening now, on the Dell charger, as the battery approaches full charge. After unplugging and replugging the Adapter from the laptop, the battery is discharging, the screen is at full brightness and the noise is a buzzin'... Note that is says there is a 45 watt adapter connected, but no Charger is detected! Go Figure.
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Please keep us posted.
Good Luck!
If any other XPS12 owners have anything else to add, of course, please do!