Hi - I need some help please. My furnace is in my garage - there are 2 brown covered wires running from the bottom part of the furnace toward the ceiling and into the wall to my house. A stray cat got into the garage and was sitting on top of my hot water tank and I noticed that one of the wires had come out of the wall and was just hanging there - it looked like it was cut in half so I don't think the cat did it... the wire inside the casing is copper colored. I have no idea what it goes to and I'm afraid to turn on my air conditioning - it didin't seem to effect the heat. What should I do?? Thanks

Repair the wire properly or call someone that knows how to do the repair.

What size are the wires compared to a pencil lead? Are they what you would consider to be small wires. What do they connect to in the furnace.
They could be old heating thermostat wires, or maybe the control wires to a humidifier that is no longer in use.

The proper term for a bundle of wires covered with plastic is a cable. A typical furnace with a split A/C system will have 3 cables. One is the power feed from the house, usually flat and may say 12-2 on it. Often there is a round brown covered 4 wire cable running inside to the thermostat. There also needs to be at least a 2 wire cable running out to the compressor . Often the same brown 4 wire cable is used. It does sound to me like as suggested, an old cable was cut off and left in place until the weight of the cat pulled it out of the wall.

If the cut cable has a number of small wires, I would turn on the system. The worst likely to happen is to burn out the control transformer. They are cheap and easy to replace. Newer ones have a fuse protecting them.