You can’t just grab any old copper wire for use on a quadcopter. Quads are subject to massive amounts of vibration, shock, and handling. Regular copper wire will quickly work-harden, stiffen, and break off. For use on quads, you want fine-strand, silicone-insulated wire–commonly referred to as “silicone wire”. The fine strands allow the wire to flex without hardening. The silicone insulation can take the heat of soldering without melting.
What the proper wire gauges are for each different power train (battery/motor/ESC) is a topic that’s up for debate but we’ll give you some guidelines here which you can scale up if you’re concerned about electrical resistance or scale down if you’re concerned about extra weight.
Flight Controller to Camera/VTX/ESC/Receiver – 30AWG is all that’s needed here and will allow the FC to free float on its rubber grommets absorbing as many vibrations as possible BEFORE they get into the gyro (heavier gauge wires hooked up to the FC tend to “hard mount” it which is bad)
Motor to ESC – For 5″ Freestyle rigs 20AWG is the industry standard and then for Sub 250 3″ Micros 24AWG is typically plenty.
ESC to Capacitor – Wire gauge isn’t the only consideration here, length also comes into play, a max length of 30mm is recommended with 18AWG wire for 5″ Freestyle rigs and then 24AWG for micros where the smaller ESC’s tend to not have enough on-board capacitance
Battery to ESC – 14AWG is the standard for 5″ freestyle and 20AWG for Sub 250