Question

Calculate the resistance of an aluminium cable of length 10 km and diameter 2.0 mm if the resistivity of aluminium is 2.7 into 10 raise to the power minus 8 ohm metre

Answer 1

Here we have the following data:

$Length = l = 10\, \, km = 10^4 \, \, m \\ \\ Diameter = d = 2.0 \, \, mm \\ \\ Radius = r = 1.0 \, \, mm = 10^{-3} \, \, m \\ \\ Resistivity = \rho = 2.7 \times 10^{-8} \, \, \Omega m$


To find the Resistance, we use the following relation:

$R = \rho \frac{l}{A} \\ \\ \\ \implies R = \rho \frac{l}{\pi r^2} \\ \\ \\ \implies R = (2.7 \times 10^{-8}) \left( \frac{10^4}{\pi \times (10^{-3})^2} \right) \\ \\ \\ \implies R = (2.7 \times 10^{-8}) \times \frac{10^4}{\pi \times 10^{-6}} \\ \\ \\ \implies R = \frac{270}{\pi} \\ \\ \\ \implies \boxed{R \approx 85.94 \, \, \Omega}$


Thus, the  Resistance is approximately 85.94 Ohms. 

Hope it helps
Purva
Brainly Community

Answer 2

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