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Need help with electricity

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data

    100[tex]\Omega[/tex] resistance wire is cut in equal parts, which are combined in parallel. They're total resistance is 1[tex]\Omega[/tex]. In how many parts the wire is cut?

    2. Relevant equations

    I guess it's something like [tex]R[/tex]=[tex]\frac{R_{1}}{N}[/tex]

    3. The attempt at a solution
    I don't have an idea how to solve it :frown: I would be very grateful if someone could help me solve this problem.
     
  2. jcsd
  3. Feb 18, 2009 #2
    Think of the resistance wire as many small resistors connected together. Because the resistors are connected together in a series, the total resistanse in the "first" situation will be

    nR=100 (1)

    Here "n" is the number of resistors (number of resistanse wire parts) and R is the resistanse of a part of resistanse wire. Since the pieces are cut in identical pieces they will also have the same "independent" resistanse.

    Further we know that if we combine the parts in parallel we get the resistanse as

    1/(R.tot)=1/(R.1)+1/(R.2)+1/(R.3)...

    Because R.1=R.2=R.3... (and so forth) we get

    1/(R.tot)=n/(R.1)

    Or

    R.tot=R=n (2)

    Again, R.1=R.2=R.3 because the pieces are identical

    Solving for (1) and (2) gives that we have 10 pieces.
     
  4. Feb 18, 2009 #3
    Sorry for my hasty reply, the second eqation should be

    R.tot=R/n

    otherwise it's fine
     
  5. Feb 18, 2009 #4
    Thank you very much, Ofey!
     
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