resistance of a wire.

Discussion in 'Homework Help' started by strantor, Aug 9, 2011.

  1. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    I'm reading this book.
    It has a little quiz at the end of each chapter. one of the questions is
    "A wire is replaced with one that is twice as long and one half the diameter. It's resistance will be:
    A. one-fourth
    B. four times
    C. eight times
    D. the same"

    My answer was B but it is saying the answer is C. Am I missing something or is the book wrong?
     
  2. MrChips

    Moderator

    Oct 2, 2009
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    The area of a circle increases as the square of the radius.
     
    strantor likes this.
  3. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    DOH! thanks
     
  4. someonesdad

    Senior Member

    Jul 7, 2009
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    In case others don't see the point, the resistance of a piece of wire is

    R = \rho \frac{L}{A}

    where ρ is the resistivity of the wire, L is its length, and A is its cross-sectional area. If the wire is round, the area is expressed as the square of the radius.
     
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