1. Not finding help here? Sign up for a free 30min 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!

Finding the Resistance of a cone

  1. Jul 15, 2011 #1
    1. The problem statement, all variables and given/known data

    A solid truncated cone is made of a material of resistivity 5.10 Ohm*m. The cone has a height h = 1.16 m, and radii a = 0.34 m and b = 0.84 m. Assuming that the direction of current is parallel to the axis of the cylinder, what is the total resistance for this cone? (Use "Ohm" as your units.)

    prob09.gif

    Hint: You have to do an integral. Regard the cone as made of a stack of pancake-shaped resistors (of varying radius) in series. The thickness of each pancake is dx and you integrate from x = 0 to x = h. You need to work out a formula for the dependence of pancake radius r on x.

    2. Relevant equations

    R= rho*L/A
    Where rho=resistivity

    3. The attempt at a solution

    I know that to find the resistance I need some Length divided by area of each infinite number of resistant pancake shape discs through the cone. The bounds of the integral are going to be 0 to h but I am not sure what to integrate. I know that both radius and area are changing but I am not sure how to integrate that. I know that rho is a constant so it can be taken out of the integral and will be multiplied to the result of the integral.

    Please help me find the formula that relates dx to radius so that I can integrate that and than multiply it by the resistivity to get the resistance of the cone.
     
  2. jcsd
  3. Jul 15, 2011 #2
    never mind i found that (0,a) and (h,b). The radius than equals pi((b-a/h)x +a)^2. Now i can easily set up the integral.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding the Resistance of a cone
  1. Finding Resistance (Replies: 2)

  2. Find the resistance? (Replies: 6)

Loading...