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A resistive wire is stretched till its length is increased by 100%. Due to the consequent decrease in diameter, the change in the resistance of the stretched wire will be ______.

Asked in GSEB Board July 2015 · Resistance of a wire and stretching

• (1) 300%
• (2) 200%
• (3) 100%
• (4) 50%

Step-by-step solution

Why the other options are wrong

• (2) Comes from adding the two effects instead of multiplying them: doubling the length gives +100% and halving the area gives another +100%. Resistance goes as ℓ/A, so the factors multiply: 2×2 = 4, a rise of 300%.
• (3) Counts only the longer length (R∝ℓ, so R doubles). The volume of the wire is fixed, so its cross-section halves at the same time and doubles R once more.
• (4) No single slip produces 50%. Sanity check: at fixed volume R∝ℓ², so ℓ→2ℓ gives R→4R, a rise of 300%.

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