Question

A wire of radius r has resistance R.If it is stretched to a wire of radius r/2, then the resistance of the wire becomes

• A. 2R
• B. R
• C. 16 R
• D. $Zero$

Answer 1

The correct option is C 16 R

Given: A wire of radius $r$ has resistance $R$. If it is stretched to a wire of radius $\frac{r}{2}$

To find the resistance of the wire

Solution:

Let resistance of the wire be $R$, area be $A$ and length be $L$

according to the given criteria,

$r_1=\frac{r}{2}$

Hence, new area becomes $A_1=\frac{A}{4}$ as area is proportional to square of the radius.

Therefore, the new length becomes $L_1=4L$

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

So new resistance is

$R_1=\rho \frac{L_1}{A_1}⟹R_1=\rho \frac{4L}{\frac{A}{4}}⟹R_1=16\rho \frac{L}{A}⟹R_1=16R$