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Resistance of wires in parallel

  1. Jun 9, 2013 #1
    1. The problem statement, all variables and given/known data
    My car has rear defrosters that are made of 13 wires embedded into the rear window. They can melt a thin layer of ice, roughly 2.25*10^-2 kg worth, in two minutes. These wires are all in parallel and are connected to the 12V battery of my car. Each is about 1.25m long and has a resistivity of 9.00*10^-8 Ω*m. What is the cross sectional area of each wire?


    2. Relevant equations
    R=ρL/A
    Q=mLf
    P=Q/t


    3. The attempt at a solution
    So, I submitted this hw a while back. My instructor finally posted solutions. In the solutions, he has written Rtotal=[itex]\frac{R^{12}}{13}[/itex], which he uses throughout his solution. My question is: why would the resistances be multiplicative? My thought is it would look like this: Rtotal=[itex]\frac{R}{13}[/itex]. Thank you for your time.
     
  2. jcsd
  3. Jun 9, 2013 #2

    CWatters

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    I agree with you about Rtotal = R/13 if R is the resistance of each wire.

    Perhaps post his whole solution?
     
  4. Jun 9, 2013 #3
    Here's his solution:
     

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  5. Jun 9, 2013 #4

    CWatters

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    I still think you are right. It should be just the standard equation for resistors in parallel ..

    Rtotal = 1/(1/R1 + 1/R2... +1/Rn)

    If R1 = R2 = RN = R

    then

    Rtotal = 1/(13/R) = R/13

    Simples.
     
  6. Jun 9, 2013 #5

    CWatters

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    I haven't worked through the rest of the problem but I'm surprised using R13 gives a reasonable answer.

    Time for bed here.
     
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