Thinner wires (of smaller area) are of larger resistance than those thicker wires (of larger area). Think of the area as parallel connection of resistors for example let 1/Rt = 1/10 + 1/10 then Rt = 5Ω as an example for smaller area wire. Now for larger area wire 1/Rt = 1/10 + 1/10 + 1/10 then...