Electrical wires are designed to carry current from one element to another. Most are made out of copper, which conducts electricity with very little resistance. If a wire is not long enough, you can splice it onto another. Provided you make a clean connection, the joint between the two wires will add only a little resistance. As long as you insulate the splice to prevent it from shorting, an extended wire will function just like a single wire.
Strip about 1 inch of insulation off of the wire you want to extend. Strip an inch of insulation off a wire of similar thickness. Make a thin incision in the insulation along the wire from 1 inch down its length to the end. Peel back the insulation.
Hold the bare end of the wire so that it crosses the bare end of the extension wire in an "X." Twist the end of each wire around the other wire to form a single twisted wire. The wires should join tightly with no gaps between them. This is called a Western Union splice, and it's one of the strongest ways to join two wires.
Plug in a soldering iron and let it heat up for two minutes. Touch the end of a braid of lead core solder to the iron for just long enough for it to smoke and a small bead to form on the tip of the soldering iron.
Touch the tip of the iron to the center of the spot where the wires join. Touch the solder to the wire right across from or next to the soldering iron. The rosin will smoke and solder will flow onto the wires. Hold the solder onto the wire until a thin layer of solder covers the spot where the two wires join. Do not hold it for long enough for a thick glob of solder to build up.
Allow the wires to cool for about a minute. Wrap the connection in electrical tape. There should be no wire showing through the tape.