Assume we have a straight piece of wire with two end points [itex]A[/itex] and(adsbygoogle = window.adsbygoogle || []).push({});

[itex]B[/itex] and with length [itex]L[/itex] where [itex]x_{A}=0[/itex] and [itex]x_{B}=L[/itex]. The wire

has non-ohmic resistance and hence the current is not proportional

to the potential difference, i.e. [itex]\left(V_{A}-V_{B}\right)[/itex]. In

fact the current is a function of the voltage at [itex]A[/itex] and [itex]B[/itex], that

is [itex]I=f\left(V_{A},V_{B}\right)[/itex].

I know [itex]f[/itex] and hence I know the current. However, I do not know [itex]V[/itex]

as a function of [itex]x[/itex] [itex]\left(0<x<L\right)[/itex]. I tried several mathematical

tricks, mainly from the calculus of variation, trying to find [itex]V\left(x\right)[/itex]

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 [itex]V\left(x\right)[/itex].

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Non-linear problem

**Physics Forums | Science Articles, Homework Help, Discussion**