The masses of the wires of copper are in the ratio $1 : 3 : 5$ and their lengths are in the ratio $5 : 3 : 1$ . The ratio of their electrical resistances is:

$5 : 3 : 1$

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$125 : 15 : 1$

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$1 : 15 : 125$

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$1 : 3 : 5$

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Solution

The correct option is B
$125 : 15 : 1$

$R = \frac{ρ l}{A} \frac{l}{l} = \frac{ρ l^{2}}{V} \frac{ρ}{ρ} = \frac{ρ^{2} l^{2}}{m}$
(Volume $=$ Area $\times$ Length)

$R_{1} : R_{2} : R_{3} = \frac{l_{1}^{2}}{m_{1}} : \frac{l_{2}^{2}}{m_{2}} : \frac{l_{3}^{2}}{m_{3}} R_{1} : R_{2} : R_{3} = \frac{(5)^{2}}{1} : \frac{(3)^{2}}{3} : \frac{(1)^{2}}{5} R_{1} : R_{2} : R_{3} = 25 : \frac{9}{3} : \frac{1}{5} R_{1} : R_{2} : R_{3} = 125 : 15 : 1$

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Similar questions

The masses of three wires of copper are in the ratio of 1:3:5 and their lengths are in the ratio 5:3:1. The ratio of their electrical resistance is :

5 : 3 : 1

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Masses of copper wires are in ratio 1:3:5 and lengths of ratio 5:3:1 . Whats the ratio of their electrical resistances ?

1 : 3 : 5

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