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2 Parallel connected cables resistance.Going from Diamater (mm) to m^2?

  1. Mar 27, 2012 #1
    A load taking 18.2A is supplied by aluminum and copper cables connected in parallel. The lengths of the copper and aluminium cables are 78m and 64m respectively. The diameter of the aluminium 1.8mm and that of the copper 2.1mm . The resistivity abd copper is 0.018uOHMm (Ohm.meter) and 0.031uOHMm (Ohm.meter) respectively. Calculate the following:

    a. The current in each cable
    b. The voltage drop across each cable.
    c. Power dissipation in each cable.

    Now I think if I could get the total resistance of both cables I could just handle them as if they where Resistors and work out all the questions but cant seem to remember how to m^2 of the cables from their current mm reading.

    Think if I could do that it would be easy to work out R with R=l.p/a formula were l = meter , a = cross section (m^2) , p = (Ohm.Meter)

    Please help.
     
  2. jcsd
  3. Mar 27, 2012 #2
    that is how you go about it. Be careful.... they have given diameter and cross section area = pi r^2
     
  4. Mar 27, 2012 #3
    Ok so I came up with this..

    ITS a huge mess

    Aluminium Cable = R1
    Copper Cable = R2
    I =18.2A
    R1s = 78m
    R2s= 64m
    R1a = r^2 π=(0.9)^2 (π)= 2.54mm^2÷1000=0.00254421m^2
    R2a = r^2 π=(1.05)^2 (π)= 3.4629525mm^2÷1000=0.0034629525m^2
    R1Ωm= 0.018μΩm ×〖10〗^(-6)=0.000000018Ωm
    R2Ωm= 0.031μΩm ×〖10〗^(-6)=0.000000031Ωm
    R1=78(0.000000018 )/((0.00000254421) )=0.9138=913.8mΩ
    R2=64(0.000000031)/((0.0000034629525) )=0.332664=332.66mΩ
     
  5. Mar 27, 2012 #4

    gneill

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    Staff: Mentor

    When converting mm2 to m2 it is important to remember that there are a million square mm in a square meter; a thousand for each meter and a square meter is 1m x 1m.

    Also, it looks like you've interchanged the resistivities of the metals. Copper should be the better conductor, so its resistivity should be smaller.
     
    Last edited: Mar 27, 2012
  6. Mar 27, 2012 #5
    Im sorry I might sound stupid but im confused.
    So you cant just go 2mm^2/1000 = 0.002m^2 ?
    Should then say 2mm/1000*1000 ?
    Wouldnt that just complicated question even further?

    Thanks for the replies :)
     
  7. Mar 27, 2012 #6

    gneill

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    Staff: Mentor

    It is what it is :smile:. No matter what it does to the question, there are a million square millimeters in a square meter! By the way, a million can be written as 106.

    Scientific notation was invented to clean up all this leading zero nonsense. It's a great tool that you should get used to.
    Glad to be of help.
     
  8. Mar 27, 2012 #7
    So 2.54mm^2 would be 2.54mm^2 x10^-6 = 0.00000254m^2
     
  9. Mar 27, 2012 #8

    gneill

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    Staff: Mentor

    Unit conversions are often spelled out in the following manner, by multiplying by ratios. Each ratio has a true value of one, being the ratio of a number of units equal in "value" to some other number of units. Thus if there are one million mm2 in one meter2, then:

    $$2.54\; mm^2 \times \frac{1\; m^2}{10^6\;mm^2} = 2.54\times10^{-6}\; m^2$$

    Notice how all the work ends up being cancelling out the units from numerators and denominators and adding up the exponents. No need to muck around with decimal places.
     
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