When a wire is compressed and its radius becomes 2R then its resistance will be:
Correct answer: C. 1/16R
- A. 16R
- B. 4R
- C. 1/16R
- D. 1/4R
Explanation
Resistance R of a wire is given by the formula R = ρ(L/A), where ρ is resistivity, L is the length, and A is the cross-sectional area. When a wire's radius is doubled to 2R, its cross-sectional area A becomes π(2R)^2 = 4πR^2, which is 4 times the original area. Since resistance is inversely proportional to the cross-sectional area, the resistance decreases by a factor of 16, making the new resistance 1/16 of the original. Thus, Option C is correct. Options A, B, and D do not correctly account for the change in cross-sectional area.
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