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Q.

Two different wires have specific resistivity, 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

$8 : 27$

c

$9 : 16$

d

$27 : 8$

answer is B.

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Detailed Solution

Given that

$ρ_{1} : ρ_{2} = 3 : 4, l_{1} : l_{2} = 2 : 9 A_{1} : A_{2} = 8 : 27 \frac{R_{1}}{R_{2}} = \frac{ρ_{1}}{ρ_{2}} \times \frac{l_{1}}{l_{2}} \times \frac{A_{2}}{A_{1}} \frac{R_{1}}{R_{2}} = \frac{ρ_{1}}{ρ_{2}} \times \frac{l_{1}}{l_{2}} \times \frac{A_{2}}{A_{1}} \frac{R_{1}}{R_{2}} = \frac{9}{16}$

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