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The resistance of a magazine wire of $1 {mm}^{2}$ cross-sectional area is $15 Ω$ . The resistance of magazine wire of same length but of a cross-section of $3 {mm}^{2}$ is

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10 Ω

12 Ω

15 Ω

5 Ω

answer is C.

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Detailed Solution

R = \frac{ρ L}{A}

$A = 1 m m^{2}$

$R_{1} = 15 Ω$

$A_{2} = 3 m m^{2}$

$R_{2} = ?$

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

$\frac{R_{1}}{R_{2}} = \frac{A_{2}}{A_{1}}$

$\frac{15}{R_{2}} = \frac{3}{1}$

$R_{2} = \frac{15}{3}$

$R_{2} = 5 Ω$

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