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Q.

Calculate the electrical conductivity of the material of a conductor of length 3 m, area of cross–section $0 .02 {mm}^{2}$ having a resistance of $2 Ω$ .

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a

70 \times 10^{6} Ω^{- 1} m^{- 1}

b

60 \times 10^{6} Ω^{- 1} m^{- 1}

c

75 \times 10^{6} Ω^{- 1} m^{- 1}

d

65 \times 10^{6} Ω^{- 1} m^{- 1}

answer is D.

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Detailed Solution

Here $l = 3 m, R = 2 Ω$

$A = 0 .02 {mm}^{2}$

$A = 0 .02 \times 10^{- 6} m^{2}$

Electrical conductivity $(σ) = \frac{1}{Resistivity} = \frac{1}{ρ} = \frac{l}{RA}$

$σ = \frac{3}{2 \times 0 .02 \times 10^{- 6}}$

$σ = 75 \times 10^{6} Ω^{- 1} m^{- 1}$

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