Results 1 to 2 of 2

Math Help - Non-linear problem

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    48

    Non-linear problem

    Assume we have a straight piece of wire with two end points A and
    B and with length L where x_{A}=0 and x_{B}=L. The wire
    has non-ohmic resistance and hence the current is not proportional
    to the potential difference, i.e. \left(V_{A}-V_{B}\right). In
    fact the current is a function of the voltage at A and B, that
    is I=f\left(V_{A},V_{B}\right).

    I know f and hence I know the current. However, I do not know V
    as a function of x \left(0<x<L\right). I tried several mathematical
    tricks, mainly from the calculus of variation, trying to find V\left(x\right)
    but I did not get a sensible result. Can any one suggest a method
    (whether from the calculus of variation or other branches of mathematics)
    to solve this problem and obtain V\left(x\right).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2011
    Posts
    246
    Thanks
    58

    Re: Non-linear problem

    Hi !
    The general solution, only based on the first wording, is :
    V(x) = Va +(f(x)-f(xa))(Vb-Va)/(f(xb)-f(xa)) or V(x) = Va +(f(x)-f(0))(Vb-Va)/(f(L)-f(0))
    where f(x) is any continuous function.
    You cannot determine what kind of function f(x) is without a descriptive physical model for the electrical behaviour from A to B.
    Last edited by JJacquelin; April 12th 2013 at 10:51 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Algebra Linear maps dealing with linear independence.
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: March 22nd 2013, 02:02 PM
  2. Linear Algebra Problem, Linear Transformation
    Posted in the New Users Forum
    Replies: 0
    Last Post: July 12th 2012, 05:06 AM
  3. Replies: 7
    Last Post: October 10th 2011, 03:06 PM
  4. Dual problem for linear programming problem
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: March 26th 2011, 04:08 PM
  5. Replies: 1
    Last Post: February 29th 2008, 09:19 PM

Search Tags


/mathhelpforum @mathhelpforum