Question

1-A piece of copper wire is 500 ft long and is 0.005" in diameter. What is the resistance of the piece of wire from end to end?

2-How much larger would the diameter of a length of Aluminum wire have to be to have the same resistance as the same length of Copper wire?

Answer 1

1)We know that,

R = rho L/A

rho(Cu) = 1.68 x 10^-7 ; L = 500 ft = 152.4 m ; d = 0.005 in = 0.000127 m

A = pi r^2 = 3.14 x (0.000127)^2 = 5.06 x 10^-8 m^2

R = 1.68 x 10^-8 x 152.4/(5.06 x 10^-8) = 50.6 Ohm

Hence, R = 50.6 Ohm

2)d = ? L = 152.4 m ; R = 50.6 Ohm ; rho(Al) = 2.65 x 10^-8

Using, R = rho L/A, we get

A = pi r^2= rho L/R = 2.65 x 10^-8 x 152.4/50.6 = 7.98 x 10^-8

r^2 = 7.98 x 10^-8/3.14 = 2.54 x 10^-8 m^2

r = sqrt (2.54 x 10^-8) = 0.000159 m

d = 2r = 2 x 0.000159 = 0.000318 m

Hence, d = 0.000318 m = 0.001 in