Question Detail
Question
If the resistance of a wire is R, and the wire is stretched to double its length, then its new resistance is:
Correct Answer
Option D is the correct answer.
Detailed Explanation
The resistance of a wire is given by R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. When a wire is stretched, its volume (V = AL) remains constant.If the length is doubled (L' = 2L), then the new area (A') must be half the original area (A' = A/2) to keep the volume constant.The new resistance R' is then:R' = ρL'/A' = ρ(2L)/(A/2) = ρ(4L/A) = 4 * (ρL/A) = 4R.So, if the original resistance was R, the new resistance is 4R.
Hint
Remember that the volume of the wire remains constant when it is stretched. How does the cross-sectional area change if the length doubles?