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Electricity; Calculating Resistance.

  1. Jan 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Calculate the resistance of a strand of aluminium wire of diameter 4.0mm and length 1.0m, given its resistivity is 2.5*10^-8 Ωm. What would be the resistance per meter of 50 strands of this wire, using the strands in parallel as a cable?


    2. Relevant equations
    ∏d^2/4 for area
    ρ=RA/L,
    Where ρ = Given resistivity
    R= Resistance
    A= Cross sectional Area
    L= Length


    3. The attempt at a solution

    4.00mm Diameter → 4*10^-3 Converted to Meters
    Length = 1m
    Resistivity = 2.5*10^-8 Ωm

    So I found out the Area using ∏d^2/4;∏*(4*10^-3)/4 which = 1.26*10^-5 m^2

    Then I used the formula
    ρ=RA/L,
    rearranging for R,
    ρL/A = R

    and subbing in the values;

    2.5*10^-8 * 1 /1.26*10^-5

    which gives an answer of 1.989*10^-3 Ωm^-1

    thus i multiplied it by 50 which gives a final answer of 0.09945

    However my answer differs from the answer of the book which is given as 4.99Ωm^-1

    Thanks for any help!
     
  2. jcsd
  3. Jan 17, 2012 #2

    BruceW

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    Homework Helper

    You've got it right up to here, so this is effectively resistance per length of one strand. And the question says that there are 50 of these strands in parallel, so now you've got to work out the total resistance of the cable due to parallel strands.
     
    Last edited: Jan 17, 2012
  4. Jan 17, 2012 #3
    The answer in the book looks wrong..... are you certain you read it correctly.
    I also got the resistance/m of 1 strand to be 1.98 x 10^-3
    50 of these in PARALLEL will not have a resistance of 4.99 Ωm^-1
    Is there a power of 10 missing somewhere?
     
  5. Jan 17, 2012 #4
    I've tried to calculate the resistors in paralell;

    1/r = 50 * 1/1.989*10^-3

    R= 3.97*10^-5

    which is still far from the answer, maybe the book is wrong?
     
  6. Jan 17, 2012 #5

    BruceW

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    I got 3.97*10^-5 as well, so maybe the book is wrong...
     
  7. Jan 17, 2012 #6
    I get the same as you (your original text book answer did not have a 10^-5 in it !!!!)
    The text book is wrong but I cant see an obvious error.
    One thing you can be sure of, when resistors are in parallel the combined resistance must be less than any of the single resistors.
    Cheers
     
  8. Jan 18, 2012 #7

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi FlyingSpartan! Welcome to PF! :smile:

    (try using the X2 icon just above the Reply box :wink:)
    hmm :rolleyes: … 4.99/3.97*10-5 = 1.26*104

    that's the area! (times 10-to-the-something) :redface:

    clearly something's gone very wrong here! :smile:
     
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