A wire of length 1 m and diameter 0.2 mm has a resistance of $100 Ω$ . Calculate the specific resistance of the material of the wire (in ohm – m)

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$2 \times 10^{- 6} Ω m$

$3.14 \times 10^{- 6}$ $Ω m$

$2 \times 10^{- 9} Ω m$

$10^{- 8} Ω m$

answer is B.

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Detailed Solution

$G i v e n t h a t : l = 1 m,$

$r = 0.1 mm = 0.1 \times 10^{- 3} m$ $= 10^{- 4} m$

$R = 100 Ω$

$R = \frac{ρ l}{A}$

$100 = ρ \times \frac{1}{π r^{2}}$

$100 = ρ \times \frac{1}{3.14 \times 10^{- 8}}$

$ρ = 3.14 \times 10^{- 6} Ω m$

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