A 1-mile-long copper wire has a resistance of 10 ohms.?

Question

What will be its new resistance when it is shortened by (a) cutting it in half or (b) doubling it over and using it as "one" wire?

Answer 1

The equation for resistance is R = ρ(L/A) , where 'L' represents the length of the wire, 'A' represents the cross-sectional area of the wire and 'ρ' represents the resistivity of the material.

Since the same material (copper) is used, ρ is a constant. Therefore, the resistance is directly proportional to L and inversely proportional to A. More about proportions at http://hsphysicslab.blogspot.com/2007/05/relationship-between-variables-part-i.html .

The solution to the question above:
(a) The length decreases by half, so the resistance decreases by half too.
(b) Doubling over doubles the cross-sectional area of the wire, so the resistance decreases by half.

EDIT: For (b), I forgot mentioning the length decreases by half also when doubling over. See sojsail's extension to my answer below.

Answer 2

Papyrus might have meant this but let me add to what he said for b)

b) Doubling over doubles the cross-sectional area of the wire, so the resistance decreases by half. And since it's now also 1/2 as long, the net affect is the resistance decreases by 1/4.

Answer 3

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