Q 12-03-084JEE MainJEE Main 2024 (6 Apr, Shift 1)Easy
A wire of resistance $R$ and radius $r$ is stretched till its radius becomes $r/2$. If the new resistance of the stretched wire is $xR$, then the value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 16
The volume stays the same, so halving the radius makes the area $\dfrac14$ and the length $4$ times.
$$R' = \rho\frac{4l}{A/4} = 16R \Rightarrow x = 16$$
Solution by Sreeraj P, M.Sc Physics