[Richard Wallace]

Wire with larger cross section has less electrical resistance per unit of length, and therefore drops less voltage and dissipates less power than wire with smaller cross section. In Europe and most other parts of the world, wire cross section is expressed in square millimeters. In the US it is more often expressed in AWG (American Wire Gage) units, a logarithmic scale defined by this formula:

AWG = 10 + (10 * log10(R)), where R is resistance per unit length, measured in Ohms per thousand feet of wire.

So 1000 feet of 10 AWG wire is equivalent to a one Ohm resistance. Scaling to dimensions more appropriate to FRC, ten feet of 10 AWG wire is equivalent to a 0.01 Ohm resistance. A current of 40 Amperes flowing in that wire will create a 0.4 Volt drop, and dissipate 16 Watts. The same 40 Amperes flowing in ten feet of 12 AWG wire will create a 0.63 Volt drop, and dissipate 25 Watts.

So using 10 AWG instead of 12 AWG keeps your wiring cooler and makes more power available to your motors; the trade off is higher cost and weight of the thicker wire.

My team uses 10 AWG for our 40 Ampere circuits.