Question

If a wire of resistance $R$ is stretched to double of its length, then the new resistance will be

• A. $ \frac{R}{2} $
• B. $ 2R $
• C. $ 4R $
• D. $ 16R $

Answer 1

Answer: (C)

If a same wire is stretched, its length increases but cross-sectional area decreases. When same wire is stretched,
$ R \propto l^{2} $
$\therefore \frac{R^{\prime}}{R}=\left(\frac{l^{\prime}}{l}\right)^{2} $
Here : $ l^{\prime}=2 l $
$\therefore \frac{R^{\prime}}{R}=\left(\frac{2 l}{l}\right)^{2}=4 $
$\Rightarrow R^{\prime}=4 R$