Question

If a wire is stretched such that it's radius is reduced to 1/nth of its original values then

• A. Resistance increases $n^4$ times
• B. Resistance decreases $n^4$ times
• C. Resistance increases $\frac{1}{n^4}$ times
• D. All

Answer 1

The correct option is A Resistance increases $n^4$ times

Resistnace of the wire initially $R=\frac{\rho L}{A}$ where $L=V/A$

$⟹$ $R=\frac{\rho V}{A^2}=\frac{\rho V}{{\pi }^2{r}^4}$ $(\because A=\pi r^2)$

Now its radius is reduced such that new radius $r^{\prime }=r/n$

Thus resistance of the wire $R^{\prime }=\frac{\rho V}{{\pi }^2(r/n{)}^4}=n^{4}R$

Hence resistance becomes $n^4$ times the initial resistance.