Suppose the conducting wire (with resistance R) was replace with one of the same material but has its dimension doubled (the length and the radius having twice their original value. What is the new resistance in comparison to the previous resistance?

Question

Physics

Broderick Hardy

5 June, 16:43

Suppose the conducting wire (with resistance R) was replace with one of the same material but has its dimension doubled (the length and the radius having twice their original value. What is the new resistance in comparison to the previous resistance?

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Bronson Gray · Answer 1

Resistance of a wire is directly proportional to its length and inversely proportional to the square of its radius.

Thus, if the length is doubled, and the radius is halved:

R₂ = 2R₁ / (1/2) ²

R₂ = 8R₁

Therefore the resistance increases eight times.