I am adding a new outlet and switch and my existing wire in the wall is about a foot short. Can I splice another foot if wire to that to make it long enough?
The National Electrical Code forbids making splices in a wiring system anywhere but in a listed box (or, in some cases, a conduit body). The easiest way to remain code compliant (and SAFE) would be to spend a few bucks for enough cable to reach the new location. The conductor size depends on the Ampacity requirements of the circuit you are installing the switch on. A 15 Amp circuit requires a minimum of #14 AWG conductors, and a 20 Amp circuit requires a minimum of #20 AWG conductors. DO NOT install wiring that is smaller than your existing conductor size. The NEC allows fishing of Type NM (Romex or rope), Type AC (BX), and Type MC Cable assemblies; you can also fish Type FMC (Greenfield or flex) Conduit. I recommend always pulling an equipment grounding conductor when using Type FMC conduit. Since I don't know how far this extension is from the junction box, I would say you must pull a green insulated or bare copper equipment grounding conductor, sized the same as the circuit conductors. Also remember that if you use any of the metallic sheathed cables, or the Flexible Metal Conduit, you must use 1/2 to feed a receptacle, 3/8 is not allowed. If you use cut-in, or old-work, type boxes; this project should not take too long or be too costly. Just be sure to do it right. If you have any doubts, hire a qualified, licensed electrical contractor.
If you can snake the wire through, you should be able to splice into the receptacle box up through the switch to the light. Don't see a reason to come back down to another receptacle as this will connect it in parallel with the circuit. Make sure you secure the power to those boxes for safety's sake though!!!
As a couple of the others have said, NO you can not, it has to be spliced in a box, and be accessible later. no wire nuts and tape, that won't cut it either. What's with the 110 volt wire, never seen that one before,we use the same wire for 120 volt or 240 volt circuits, the number of conductors just vary. There is a product out there that you crimp on the ends of romex for number 12 and number 14 that is like a plug, they use them on double wide trailer houses, but they really are not to be concealed, none of the electrical inspectors around here would let you use that that way. Cut in a box and splice in the box and go to where you want. Just be care full of the advice you see here on yahoo there are very few who really know anything about anything that has to do with electrical in the real world here, just make sure your fire insurance is paid up and current, we got experts here than think a 10/3 romex is okay on a 50 amp breaker, so if in doubt call an electrician, IBEW has electricians all over the country.
How To Splice Electrical Wire
Add a new outlet, and run your new wire from that. Electrical inspector, since when can you run 20 amps on 20 gage wire?Don't you mean # 12.