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Question
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 m
Diameter of the cable wire, d = 2.0 mm
Radius of the cable wire, r = 1.0 mm = 1.0 × 10−3 m
Area of cross-section, A = πr2
= π(1.0 × 10−3)2
= π × 1.0 × 10−6
Resistivity of the aluminium cable wire = 27 × 10−8 Ω m.
Let the resistance of the aluminium cable be R.
We know that `R = (rho l)/A`
`R = (27 xx 10^-8 xx 10^3 xx 10)/(pi xx 10^-6)`
`R = (27 xx 10^-8 xx 10^4)/(3.14xx10^-6)`
`R = (27 xx 10^2)/pi`
R = 86 Ω
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