  We study the behavior of steady state voltage potentials in two kinds of
bidimensional media composed of material of complex permittivity equal to 1
(respectively $\alpha$) surrounded by a thin membrane of thickness $h$ and of
complex permittivity $\alpha$ (respectively 1). We provide in both cases a
rigorous derivation of the asymptotic expansion of steady state voltage
potentials at any order as $h$ tends to zero, when Neumann boundary condition
is imposed on the exterior boundary of the thin layer. Our complex parameter
$\alpha$ is bounded but may be very small compared to 1, hence our results
describe the asymptotics of steady state voltage potentials in all
heterogeneous and highly heterogeneous media with thin layer. The terms of the
potential in the membrane are given explicitly in local coordinates in terms of
the boundary data and of the curvature of the domain, while these of the inner
potential are the solutions to the so-called dielectric formulation with
appropriate boundary conditions. The error estimates are given explicitly in
terms of $h$ and $\alpha$ with appropriate Sobolev norm of the boundary data.
We show that the two situations described above lead to completely different
asymptotic behaviors of the potentials.
