1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Current flowing through a copper wire

  1. Mar 27, 2010 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations
    A=ρL/R A=π r^2 P = I^2R R=V/I P=V^2/R
    v=I/nqA


    3. The attempt at a solution

    a) from A = pL/R
    r=squareroot(A/pi)=squareroot(pL/PiR)=1.046 mm

    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,
    --sweetdion
     
  2. jcsd
  3. Mar 27, 2010 #2

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    We were not given a value for R; you have left out some steps in how you got to your 1.046 mm answer.

    You have neglected the 1023 part of Avogadro's number. Also, your units conversion is wrong:

    If (1 m) = (100 cm), then
    (1 m)^3 = (100 cm)^3 = ____ cm^3 ?

    Yes, it is easiest to use 1 m and 2 W to solve the problem. Alternatively, using 2 m and 4 W, or 3 m and 6 W, etc., should give the same answer, since they all use 2 W per m.
     
  4. Mar 28, 2010 #3
    to find R i did R=V/I=0.1V/20A = .005Ω then I plugged it in to get the right answer

    thanks for your help!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook