Question

If a wire is stretched to make its length three times, its resistance will become

• A. Three times
• B. One-third
• C. Nine times
• D. One-ninth

Answer 1

The correct option is C Nine times

A wire is cylindrical in shape. When it is stretched, its length increases but volume remains the same. That means the cross-sectional area must also change.

Volume $=\pi r^{2}L=A\times L$

$L^{\prime }=3L⟹A^{\prime }=\frac{A}{3}$

We know,

$R=\frac{\rho \times L}{A}$

$R\propto \frac{L}{A}$

Hence,

$\frac{R^{\prime }}{R}=\frac{L^{\prime }}{L}\times \frac{A}{A^{\prime }}=\frac{3L}{L}\times \frac{A}{\frac{A}{3}}=9$

Hence,

$R^{\prime }=9R$