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!

Distribution between non-linear branches

  1. Jun 9, 2015 #1

    My question could be about bars and litres/sec but I'll express it as volts and ampères, mathematically it's the same puzzle for me. How do you calculate the currents in circuits when there are devices whose resistances are not linear?
    In the following network there are 3 low value linear resistances and two 3rd order polynomial devices whose functions are :

    V1 = 0.24 x I1^3 - 0.3 x I1^2) + 0.98 x I1 + 3.72
    V2 = 0.07 x I2^3 - 0.02 x I2^2) + 0.16 x I2 + 1.57

    No mathematical solution other than a successive approximation approach?

    Thanks for your help.

  2. jcsd
  3. Jun 10, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You have two cubic functions f and g, and two constant R and V, and you wish to solve
    f(i1)=g(i2), f(i1)+R(i1+i2) = V. Yes?
    Writing x = i1,
    f(x) = g(V/R-f(x)/R-x)
    Expanding that will give a polynomial with powers of 6.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook