A wire of length L and resistance R is stretched to get the radius of cross-section halved. What is new resistance?

$For a wire of length \text{'}L\text{'} and area of cross section \text{'}A\text{'} the resis\tan ce R can be expressed as$

$R = \frac{\rho L}{A}$
When it is stretched, its radius reduces to half hence the area of cross section = $\frac{A}{4}$ and length would be double.

$New Resis\tan ce, R\text{'} = \rho \frac{\left(2L\right)}{\left({\displaystyle \frac{A}{4}}\right)}$

$R\text{'} = \frac{8\rho L}{A}$

$R\text{'} = 8 R$