Compare the resistance of two wires of same material. Their lengths are in the ratio $2 : 3$ and their diameters are in the ratio $1 : 2$ .

8:3

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4:3

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8:2

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4:2

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Solution

The correct option is A 8:3
$R = ρ \frac{L}{A} = ρ \frac{4 L}{π D^{2}}$

$⟹ R \propto \frac{L}{D^{2}}$

$⟹ \frac{R_{1}}{R_{2}} = \frac{\frac{L_{1}}{D_{1}^{2}}}{\frac{L_{2}}{D_{2}^{2}}}$

$⟹ \frac{R_{1}}{R_{2}} = \frac{L_{1}}{L_{2}} \frac{D_{2}^{2}}{D_{1}^{2}}$

$⟹ \frac{R_{1}}{R_{2}} = \frac{2}{3} \times (2)^{2}$

$⟹ R_{1} : R_{2} = 8 : 3$

Answer-(A)

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