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 : $l^{\prime }=2l$
$\therefore \frac{R^{\prime }}{R}={\left(\frac{2l}{l}\right)}^2=4$
$\Rightarrow R^{\prime }=4R$