  We describe the asymptotic behaviour of the minimal inhomogeneous
two-capacity of small sets in the plane with respect to a fixed open set
$\Omega$. This problem is governed by two small parameters: $\varepsilon$, the
size of the inclusion (which is not restrictive to assume to be a ball), and
$\delta$, the period of the inhomogeneity modelled by oscillating coefficients.
We show that this capacity behaves as $C|\log\e|^{-1}$. The coefficient $C$ is
explicitly computed from the minimum of the oscillating coefficient and the
determinant of the corresponding homogenized matrix, through a harmonic mean
with a proportion depending on the asymptotic behaviour of
$|\log\delta|/|\log\varepsilon|$.
