= Ionic resistance of a conical pore
{title2=$\mathcal R=\rho L/(\pi ab)$}
In a one-dimensional Ohmic approximation, a linear conical frustum of <length> $L$, end <radii> $a,b>0$ and ionic resistivity $\rho$ has $r(z)=a+(b-a)z/L$. Conservation of <electric current> gives $d\mathcal R=\rho\,dz/[\pi r(z)^2]$. Integration yields the displayed resistance. Two identical opposed frusta, each of <length> $l$, have resistance $2\rho l/(\pi ab)$, whether their central junction is the wider or narrower end. Their local field profiles nevertheless differ. The approximation neglects surface conduction and resistance outside the defined pore, and is not an exact three-dimensional field solution for arbitrary wall slope.
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