- #1
JulieK
- 50
- 0
Assume we have a straight piece of wire with two end points [itex]A[/itex] and
[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 anyone 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].
[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 anyone 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].