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Q.

A uniform wire of resistance R is uniformly compressed along its length until its radius becomes n times the original radius, now the resistance of the wire becomes

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a

\frac{R}{n^{4}}

b

\frac{R}{n^{2}}

c

nR

d

\frac{R}{n}

answer is A.

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Detailed Solution

We know when a wire is compressed or stretched

$R \propto \frac{1}{A^{2}}$

$\frac{R_{1}}{R_{2}} = \frac{A_{2}^{2}}{A_{1}^{2}} = {(\frac{π r_{2}^{2}}{π r_{1}^{2}})}^{2} = \frac{r_{2}^{4}}{r_{1}^{4}}$

Here $r_{2} = n r_{1}, R_{1} = R$

$\frac{R_{1}}{R_{2}} = n^{4}$

$∴ R_{2} = \frac{R}{n^{4}}$

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