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A copper wire of cross-sectional area $0.01 {mm}^{2}$ is used to prepare a resistance of $1 k Ω$ . The resistivity of copper is $1.7 \times 10^{- 8} Ω m$ . Calculate the length of the wire

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58.82 m

588.2 m

0.58 m

5.8 m

answer is B.

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Detailed Solution

Given

$A = 0.01 \times 10^{- 6} m^{2} A = 10^{- 8} m^{2} R = 1 k Ω R = 10^{3} Ω ρ = 1.7 \times 10^{- 8} Ω m R = ρ l /A l = \frac{RA}{ρ} = \frac{10^{3} \times 10^{- 8}}{1.7 \times 10^{- 8}} l = \frac{1000}{1.7} = 588.2$

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