Question

Wire 1 has a resistance R1. Wire 2 is made of the same material, with length 1/2 as long and diameter 1/4. What is the resistance ratio R2/R1?

Answer 1

-- reduce the length of a wire to 1/2 . . . cut the resistance in half

-- reduce the diameter to 1/4 . . . reduce the cross-section area by (1/4²) . . . increase the resistance by 16x .

-- R2 = (R1) · (1/2) · (16) = 8 · R1

-- R2 / R1 = 8