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Compute the magnitude of the current density

  1. Apr 3, 2016 #1
    1. The problem statement, all variables and given/known data
    Copper and aluminum are being considered for a high‐voltage transmission line that must carry a current of 51.4 A. The resistance per unit length is to be 0.176 Ω/km. Compute the magnitude of the current density for an aluminum cable.

    2. Relevant equations
    [itex]R\quad =\quad \frac { \rho L }{ A } \\ J\quad =\quad \frac { I }{ A } [/itex]

    3. The attempt at a solution
    [itex]\frac { R }{ L } \quad =\quad 0.176\frac { \Omega }{ km } \quad =\quad 1.76x10-4\frac { \Omega }{ m } \\ \\ \frac { R }{ L } \quad =\quad \frac { \rho }{ A } \quad \quad \quad \quad \quad A\quad =\quad \frac { I }{ J } \\ \\ \frac { R }{ L } \quad =\quad \frac { \rho J }{ I } \\ \\ \frac { RI }{ L\rho } \quad =\quad J\quad =\quad 1.76x10-4\quad *\quad \frac { 51.4 }{ 2.65x10-8 } \quad =\quad 3.41x10+5\quad [/itex]

    This is marked as wrong, any tips?
     
  2. jcsd
  3. Apr 3, 2016 #2

    TSny

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    Your work looks correct to me, but you didn't include the units in your final answer.
     
  4. Apr 3, 2016 #3
    Units of J are A/m^2
    Strange, it still marks that as the wrong answer
     
  5. Apr 3, 2016 #4

    TSny

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    Hmm. I can't see anything wrong. Different references can give somewhat different values for the resistivity of aluminum. But I guess you are using the value from your textbook or notes from class. See http://hypertextbook.com/facts/2004/ValPolyakov.shtml

    Resistivity is temperature dependent, but no information about temperature is given in the statement of the problem.
     
    Last edited: Apr 3, 2016
  6. Apr 3, 2016 #5
    I can't see anything wrong either, i'll just have to ask the prof. Thanks for the help!
     
  7. Apr 3, 2016 #6

    TSny

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    OK. Please report back if there is a mistake in the calculation. I would like to know what I'm missing.
     
  8. Apr 3, 2016 #7
    Sure thing
     
  9. Apr 4, 2016 #8
    Are you sure your resistivity value is correct? Since it is both copper and aluminum, I added the resistivity values of both copper and aluminum together and got a resistivity values of 4.5x10^-8. I am not sure if that is how you combine them, but if it is, I got a value of 2.01x10^5. I hope this helps=).
     
  10. Apr 4, 2016 #9

    SammyS

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    It would be more appropriate to compare the two. Adding the resistivities makes little or no sense.
     
  11. Apr 4, 2016 #10
    Sorry, I didn't see that we were only looking for the resistivity of the aluminum cable. In that case, I think that the resistivity might still wrong because I looked it up, and it came up to be 2.82X10^-8. Not much of a difference, but try it. Sorry again.
     
  12. Apr 6, 2016 #11
    No mistake, just a slightly different resistivity
     
  13. Apr 6, 2016 #12

    TSny

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    OK, that's good to know. Thanks.
     
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