Question

A uniform wire of length $l$ and radius $r$ has a resistance of $100\Omega$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of new 2 wire will be :

• A. $100\Omega$
• B. $1600\Omega$
• C. $200\Omega$
• D. $400\Omega$

Answer 1

The correct option is B $1600\Omega$

Uniform wire length $l$

Redius $r$

Resistance$100\Omega$

If its radius = $\frac{r}{2}$

$\Rightarrow \frac{r_2}{r_1}=\frac{\frac{l_2}{A_2}}{\frac{l_1}{A_1}}$

volume remians constant

$\Rightarrow l\times \pi r^2=l\times \pi \frac{r^2}{4}$

We know, $[l=4]$

$\Rightarrow r_2=r_1\left[\frac{\frac{4}{\pi r^2/4}}{\frac{1}{\pi r^2}}\right]$

$\Rightarrow r_2=16r_1$

$\Rightarrow r_2=1600\pi$