Calculate the resistance of an aluminium cable of length $10 k m$ and diameter $2.0 m m$ if the resistivity of aluminium is $2.7 \times 10^{- 8} Ω m$ .

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Solution

$d = 10 k m = 10 \times 10^{3}$ meter
$d = 2.0 m m \Rightarrow$ radius r = 1 mm = $1 \times 10^{- 3}$ meter.
$\Rightarrow$ cross sectional area $A = π r^{2} = π \times 10^{- 6} m^{2}$
So resistance $R = \frac{P l}{A} = 2.7 \times 10^{- 8} \times \frac{10^{4}}{π \times 10^{- 6}} Ω$
$\Rightarrow R = 85.98 Ω$

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Calculate the resistance of an aluminium cable of length 10 km and diameter 2.0 mm if the resistivity of aluminium is 2.7×10−8Ωm.

d=10km=10×103 meterd=2.0mm⇒ radius r = 1 mm = 1×10−3 meter.⇒ cross sectional area A=πr2=π×10−6m2So resistance R=PlA=2.7×10−8×104π×10−6Ω⇒R=85.98Ω

Calculate the resistance of an aluminium cable of length $10 k m$ and diameter $2.0 m m$ if the resistivity of aluminium is $2.7 \times 10^{- 8} Ω m$ .