I want to mount a tablet to a wall with a charger but I don't want the charger to be visible. Can I put a normal wall outlet in the INSIDE of the wall and just plug in the charger inside the wall?
Location is Wisconsin, USA.
No. Section 314.29 of the National Electrical Code (adopted in some form in most localities in the US) requires that all outlet boxes be accessible without removing any part of the building or structure. That includes wallboard.
You could build a recessed section in the wall that has an easily removed front panel. You could install an outlet in that section, plug in the charger and then run the charging cable through a hole in that panel.
If the tablet uses a standard USB charger, you can now get outlets that have the charger built in. Then you just need to plug the low voltage USB cable into the outlet and into the tablet.
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You can use a recessed outlet to hide the wires. These were originally created so wall mounted electrical clocks can be mounted flush. They are now pretty commonly used for home theater setups where the TV is mounted to the wall, so there aren't any visible wires.
Something like this could work for your tablet setup. You would just have to make sure that there is enough room in the box to accommodate it since it leaves much less room for the wires.
As pointed out by many others at this point, direct answer to your question is No: you are not allowed to install an outlet inside a wall. All outlets and junctions must be accessible without having to modify building structure or components.
I would skip the high voltage entirely here and use Power-over-Ethernet (PoE) on Cat5e/6 cables to bring power to the tablet. This avoids the need for extra junction boxes, running 120V wiring, access panels, etc.
It's also very easy to fish Cat5e/6 through as small as 3/8" holes, making it fairly easy to run wherever you need to go. Another future benefit is that it's also relatively easy to tear out (compared to something involving 120V wiring/outlets) if you're moving or want to move or remove the tablet mount.
In your case you don't need the "data" part, so that simply wouldn't be hooked up.
The actual power supply can be anywhere the ethernet cable can reach (up to 100m/328'), ideally out of sight in the basement or with the rest of your network cabling.
The receiving end is just low-voltage, and can sit tucked behind your mount. You'll want it accessible in some way in case it breaks or something, but it doesn't fall under NEC rules.
The cheapeest way is to just use "passive" PoE, which isn't standardized, but just uses the unused pairs of 10/100 connections for power. Various kits exist, a quick search finds that you may need an adapter to convert the barrel-style DC adapter these usually have to a USB female jack.
There's a couple downsides to this: if you connect a regular ethernet device on the other end for some reason, there's a chance it could fry it. Since there are no standards on this, you should only use the pair of injector/splitter from the same source to ensure compatibility.
Some of these kits run power at 5V, so after about 15' you can get some voltage loss which will at some point cease to charge the tablet. Better ones will run at 24 or 48V and do a step-down to 5V output, so they can handle quite a bit of drop.
You also can go with actual 802.3af/at PoE. This always runs at ~48V to avoid voltage drop, negotiates power requirements (won't fry non-PoE stuff), and is an actual standard that works across manufacturers. If you already have a PoE switch with spare ports for something else or have other PoE stuff to power (eg IP camera or phone), this is probably the best option.
You can get 802.3af/at PoE injectors or switchs to provide power.
Can you do it, sure. Should you do it, no way.
As alluded to above, the obvious answer is to get a large clock receptacle (just google it), e.g., http://www.amazon.com/Arlington-DVFR2W-1-Recessed-Electrical-Paintable/dp/B001XQ4JFC -- with this one you can go to town, mount whatever you want in it.
And you'll need a 90 degree micro USB adapter to make the charging cable go away. Ebay has stuff like that.
I think you are asking the wrong question -- if you are wanting to power a low voltage device with a USB charging connection from AC Mains, then what you want is a transformer or AC/DC converter -- these are NOT outlets and can be mounted out of sight (think doorbell transformers for example).
The fact that you wire it to the device through a usb connector would not be relevant since that is a low voltage connection. Just make sure the converter/transformer is certified for in wall use.
I have resolved this problem with my inwall iPads. I simply have a recessed (in wall) mount that I cut large hole in drywall for, then I install the receptacle in the wall but easily accessible through the iPad mounting hole, then plug in charger, and stick iPad into wall inside the hole. To access the plug, I simply remove the iPad (3 minutes) and reach inside and unplug or plug in the charger, and then re-install the iPad. (3 more minutes)
Since there is no need to modify drywall or any structural part of the house its legal. (my opinion, but I see no problem)