Question

A wire of radius r has resistance R . If it is stretched to a radius of $\frac{3r}{4}$, its resistance becomes

• A. $\frac{9R}{16}$
• B. $\frac{15R}{9}$
• C. $\frac{81R}{256}$
• D. $\frac{256R}{81}$

Answer 1

Answer: (D)

$\frac{256R}{81}$

We have,

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

and

$A=\pi r^2$

when radius $=\frac{3r}{4}$ and its resistance $=\frac{R}{r}$

where $r$ is the required resistance

Then,

$\frac{R}{r}=(\frac{r_1}{r_2}{)}^4$

$\frac{R}{r}=\frac{(\frac{3r}{4}{)}^4}{r^4}$

$\frac{R}{r}=\frac{\left(\frac{81r^4}{4^4}\right)}{r^4}$

$\frac{R}{r}=\frac{81}{256}$

$⟹r=\frac{256R}{81}$