1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Electrical resistance of a paraboloid.

  1. Mar 28, 2010 #1
    1. The problem statement, all variables and given/known data
    What would the electrical resistance of a paraboloid from y = 0 to L be?


    2. Relevant equations
    [tex]R = \rho \frac{L}{A}[/tex]


    3. The attempt at a solution
    Okay, so I'll put the parabola (that would rotate into the paraboloid) into the form [tex] y = \sqrt{x}[/tex]

    The function A(x) is just the area of the circle, at distance x.

    A = [tex]\pi y^{2} = \pi x[/tex]

    I'll break the paraboloid up first into a finite sum of discs, from 0 to L.

    [tex]R = \Sigma \rho \frac{\Delta x}{A(x)}[/tex]

    ==>

    [tex]R = \int^{L}_{0} \rho \frac{dx}{\pi x}[/tex]

    ==>

    [tex]R = \frac{\rho}{\pi} \int^{L}_{0}\frac{1}{x} dx[/tex]

    This integral resolves to:

    [tex]R = [\frac{\rho}{\pi}ln(x)]^{L}_{0}[/tex]

    Natural log of 0 is undefined, so this would resolve to a numerical answer, as at the limit of x ==> 0, the area approaches zero and this means infinite resistance. But is the maths correct? Or can someone suggest a better way to actually find an answer.
     
  2. jcsd
  3. Apr 21, 2010 #2
    bump. <_<
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook