The resistance of a wire of length / and area of cross-section a is x

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The resistance of a wire of length / and area of cross-section a is x ohm. If the wire is stretched to double its length, its resistance would become:

2x ohm
0.5 x ohm
4x ohm
6x ohm
This question was previously asked in
UPSC NDA-2 – 2015
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The resistance (R) of a wire is given by R = ρ * (l/a), where ρ is resistivity, l is length, and a is cross-sectional area. If the wire is stretched to double its length (l’ = 2l), its volume (V = a * l) remains constant. So, a’ * l’ = a * l => a’ * (2l) = a * l => a’ = a/2. The new resistance is R’ = ρ * (l’/a’) = ρ * (2l / (a/2)) = ρ * (4l/a) = 4 * (ρ * l/a) = 4x.
When a wire is stretched, its length increases, and its cross-sectional area decreases while its volume remains constant. This significantly increases its resistance.
The resistance is directly proportional to length and inversely proportional to cross-sectional area. Stretching the wire affects both parameters simultaneously.

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