Q1. [1] § 11.5 FACTORS ON WHICH THE RESISTANCE OF A CONDUCTOR DEPENDS
A wire of length 'l' is gradually stretched so that its length increases to 3l. If its original resistance is R, then its new resistance will be :
- (A) 3R
- (B) 6R
- (C) 9R
- (D) 27R
Previously asked in CBSE board exam
2025 31/3/1 Q13
Generated by claude-sonnet-4-6 · 2026-06-15 06:43 · grounding rag
Model Answer
(C) 9R
When length becomes 3l, volume is conserved, so area becomes A/3. New resistance = ρ(3l)/(A/3) = 9(ρl/A) = 9R.
Source: Electricity, Section 11.5
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Explanation
Key concept: Volume of wire is conserved during stretching (V = A·l = constant).
- New length = 3l → New area = A/3
- Since R = ρl/A, new R' = ρ(3l)/(A/3) = 9·ρl/A = 9R
- Resistance scales as the square of the length multiplier when volume is conserved. Examiners expect you to state the conservation of volume step clearly.
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