Rewiring Existing Receptacle With a Shared Neutral
Hello there. I'm doing some rewiring in my circa-1948 home. Wiring is mostly the original 14-gauge 2-conductor with no ground, except for the rooms that I've already rewired.
Today I've rewired an outlet in my living room which ran off a single 15-amp circuit which powered my 55" Television, Surround Receiver, CD changer, DVD player, Tape Deck, Cable Box, VCR, two floor lamps, and wall sconces. I rewired it because I will be using an 11,000 BTU window A/C this summer, and the AC blows the fuse when the TV is on and the compressor kicks on. (I have a dedicated 240V 20A receptacle under this window, but I don't have a 240V AC, and the smallest I can find is 18,000BTU which is way too large for my 1000 square foot apartment.)
So, I rewired the existing outlet (an end-of-the-run receptacle) with 12 AWG wire and fed it back to the fuse box along with a 20A fuse. The problem is that this outlet also had a lone neutral wire running from it up in the wall where it provided a path back to the fuse box for wall sconces over my fireplace. The hot wire for the sconces comes from one of the other three living room outlets.
Is it acceptable to connect this neutral to the receptacle of my air conditioner's (now dedicated) 20A circuit as it was before? I'm sure the 12 gauge wire is large enough to handle the current traveling back to the panel from the two 9W CFL bulbs along with the air conditioner.