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Two different wires have specific resistivity's, lengths, area of cross-sections are in the ratio 3:4, 2:9 and 8:27. Then the ratio of resistance of two wires is

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a

16 : 9

b

9 : 16

c

8 : 27

d

27 : 8

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detailed solution

Correct option is B

GivenRatio of specific resistance $\frac{ρ_{1}}{ρ_{2}} = \frac{3}{4}$ Ratio of lengths $\frac{ℓ_{1}}{ℓ_{2}} = \frac{2}{9}$
Ratio of area of cross-sections $\frac{A_{1}}{A_{2}} = \frac{8}{27}$ Ratio of resistance $\frac{R_{1}}{R_{2}} = ?$
$\frac{R_{1}}{R_{2}} = \frac{ρ_{1}}{ρ_{2}} \frac{ℓ_{1}}{ℓ_{2}} \times \frac{A_{2}}{A_{1}} (∵ R = \frac{ρl}{A}) = \frac{3}{4} \times \frac{2}{9} \times \frac{27}{8} = \frac{9}{16}$

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