1. The wiring in a house must have low enough resistance so that it does not heat up too much while current is flowing. A particular copper wire needs to carry 20 A of current, and it must not dissipate more than 2 watts of power per meter of length. The resistivity of copper is ρ=1.72 x 10^-8 Ωm
a) What is the minimum diameter that the wire must have so that it doesn't heat up too much?
b) The density of copper metal is 9 g/cm^3, and the atomic mass is 63.5 g/mole. Avagadro's number is 6.022 x 10^23 atoms/mole. Assume one charge carrier per atom and determine the density of charge carries n (number of charge carriers per cubic meter) in copper.
c) A copper wire with circular cross-section with radius r=1mm carriers 1 A of current. Determine the drift velocity of the electrons in the wire.
A=ρL/R A=π r^2 P = I^2R R=V/I P=V^2/R
The Attempt at a Solution
a) from A = pL/R
b) d=9g/cm^3 x 1mol/63.5g x 6.022x10^23 charge carriers/1mol x 100 cm^3/1 m^3 = 8.535 charge carriers/m^3
c) r = .001 m
I = 1 A
v= I/nqA = 1/(8.545)(1.6x10^-19)(1.72x10^-8*1 m/.001m)= 4.257 m/s
I was unsure about the coversion from cm^3 to m^3
Also, I'm unsure about the length I am supposed to use. Should it be 1 m because the power was given to me in watts/meter?
Thanks in advance,