Answer to Question #183637 in Electric Circuits for Lianne

Question

Show all the solutions. Round off answers to two decimal places.

3. High-voltage power lines are familiar sights throughout the country. The aluminum wire used for some of these lines has a diameter of 2.5 cm. What is the resistance of 10,000 m of this wire? Resistivity = 2.83 x 10^-8 ohm-m.

Answer 1

Radius of wire, $r=\dfrac{2.5}{2}=1.25\space cm=1.25\times10^{-2} m$

Area of cross section, $A$ = $\pi r^2=4.90\times10^{-4}\space m^2$

Length of wire, $l=10,000\space m$

Resistivity, $\rho=2.83\times 10^{-8}\space ohm-m$

Resistance, $R=\rho\dfrac{l}{A}=2.83\times10^{-8}\times\dfrac{10000}{4.90\times10^{-4}}$

$R=5.77\space \Omega$