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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 27 × 10^{−8} Ωm.

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#### Solution

Length of the cable wire,

*l*= 10 km = 10000 mDiameter of the cable wire,

*d*= 2.0 mmRadius of the cable wire,

*r*= 0.1 mm = 0.0001 m = 10^{-4 }mArea of cross-section, `A=Api^2` 3.14 × 10

^{-8}m^{2}Resistivity of the aluminium cable wire = 27 × 10

^{−8}Ω m.Let the resistance of the aluminium cable be *R*.

We know that `R=l/A`

R=P/A

`R=27xx10-8xx103.14xx10-8`

`R=(27xx10^-8xx10000)/(3.14xx10^-8)`

*R* = 86 Ω

Concept: System of Resistors - Resistors in Series

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