Question

Calculate the resistance of a 5km length of aluminum overhead power coble if the cross-
sectional area of the cable is 100mm2

. Take the resistivity of aluminum to be 0.03 × 10−6Ωm.

Answer 1

$\bf{\underline{\underline{Given}}}$

$\mathsf{\small{\bigstar\: Length \: (L) = 5 \:km = 5000\: m}}$

$\mathsf{\small{\bigstar\: Area \: (A) = 100 \:mm^{2} = 100^{-3} \:m^{2}\: }}$

$\mathsf{\small{\bigstar\: Resistivity \: (\rho) = 0.03 × 10^{-6} \: Ωm}}$

$\bf{\underline{\underline{To \: find}}}$

$\mathsf{\small{\bigstar\: Resistance \: of \: aluminium\: cable\: (R)}}$

$\bf{\underline{\underline{Solution}}}$

We know that,

$\fbox{\mathsf{\red{Resistance = \rho \: \frac{L}{A}}}}$

$\mathsf{\implies\: R = \frac{0.03 × 10^{-6} × 5000}{100^{-3}}}$

$\mathsf{\implies\: R = \frac{3 × 10^{-2} × 10^{-6} × 5 × 10^{3}}{(10^2)^{-3}}}$

$\mathsf{\implies\: R = \frac{3 × 10^{-2} × \cancel{10^{-6}} × 5 × 10^{3}}{\cancel{(10^{-6})}}}$

$\mathsf{\implies\: R = 3 × 10^{-2} × 5 × 10^{3}}$

$\mathsf{\implies\: R = 15 × 10}$

$\mathsf{\implies\: R = 1.5 × 10^{2} \:Ω\: \: \green{(Answer)}}$

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Note:

$\mathsf{\green{\bigstar\: 1\:mm = 10^{-3} \: m }}$

$\mathsf{\green{\bigstar\: 1\:km = 10^{3} \: m }}$