When a wire is stretched such that its length becomes double then its resistance increases by (100 × n) %, then n
Question
When a wire is stretched such that its length becomes double then its resistance increases by (100 × n) %, then n
Solution
The resistance (R) of a wire is given by the formula:
R = ρL/A
where: ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
When the wire is stretched to double its length, the volume of the wire remains constant. So, the cross-sectional area (A) becomes half. Therefore, the new resistance (R') is:
R' = ρ(2L)/(A/2) = 4ρL/A = 4R
The increase in resistance is R' - R = 4R - R = 3R.
In percentage terms, the increase is (3R/R) * 100 = 300%.
Therefore, n = 300.
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