A wire of resistance R is stretched till its length is double that of the original wire. Then, the resistance of the stretched wire is:
Correct answer: B. 4R
- A. 2R
- B. 4R
- C. 8R
- D. 16R
Explanation
When a wire is stretched to double its original length, its cross-sectional area is reduced by half due to the conservation of volume. Resistance is calculated using the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. With the new length L' = 2L and new area A' = A/2, the resistance becomes R' = ρ(2L)/(A/2) = 4(ρL/A) = 4R. Therefore, the resistance of the stretched wire is 4R. Options A, C, and D are incorrect as they do not accurately account for the relationships between length, area, and resistance.
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