  We study Fuglede's $p$-module of systems of measures in condensers in
Euclidean spaces and on polarizable Carnot groups. We apply and generalize a
result by Rodin, which provides an explicit method for finding the extremal
function and the 2-module of a foliated family of curves in $\mathbb R^2$, to a
variety of settings. In the planar case, we apply Rodin's method to obtain
estimates for the conformal module of a parallelogram and of a ring domain
using directional dilatations. In $\mathbb R^n,$ we identify the extremal
function and compute the $p$-module of images of families of connecting curves
and of separating sets with respect to the plates of a condenser under
homeomorphisms of certain regularity. Then we calculate the module and find the
extremal measures for the spherical ring domain on polarizable Carnot groups
and extend Rodin's theorem to the spherical ring domain on the Heisenberg
group.
