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A cylindrical conductor of length *l* uniform area of cross-section A has resistance R. What should be the area of cross-section of another conductor of same material to have the same resistance.

Resistance of a conductor,

$R=\rho \frac{l}{A}\phantom{\rule{0ex}{0ex}}where,\phantom{\rule{0ex}{0ex}}\rho istheresistivityofthematerial\phantom{\rule{0ex}{0ex}}l=lengthoftheconductor\phantom{\rule{0ex}{0ex}}A=areaofcross-sectionofthematerial$

For another conductor of same material to have the same resistance, the area of cross-section can be determined in terms of its length.

Let the length of the conductor be l' and its area of cross-section be A', then

$\rho \frac{l\text{'}}{A\text{'}}=R\phantom{\rule{0ex}{0ex}}\rho \frac{l\text{'}}{A\text{'}}=\rho \frac{l}{A}\phantom{\rule{0ex}{0ex}}\frac{l\text{'}}{A\text{'}}=\frac{l}{A}\phantom{\rule{0ex}{0ex}}A\text{'}=\frac{A}{l}l\text{'}$

Regards

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