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Direct Proportion

Suppose the r...

Question

Suppose the resistance of a wire varies inversely as the area of its cross-section. Write a relation between resistance and area of cross-section

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Solution

Suppose the radius of the wire is $r$ . Then the area of its cross-section is $π r^{2}$ . If $R$ is the resistance, we are given
$R \propto \frac{1}{π r^{2}}$
Hence
$R = \frac{k}{π r^{2}}$ or $k = R π r^{2}$ .

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