  A graph can be regarded as an electrical network in which each edge is a
resistor. This point of view relates combinatorial quantities, such as the
number of spanning trees, to electrical ones such as effective resistance. The
second and third authors have extended the combinatorics/electricity analogy to
higher dimension and expressed the simplicial analogue of effective resistance
as a ratio of weighted tree enumerators. In this paper, we first use that ratio
to prove a new enumeration formula for color-shifted complexes, confirming a
conjecture by Aalipour and the first author, and generalizing a result of
Ehrenborg and van Willigenburg on Ferrers graphs. We then use the same
technique to recover an enumeration formula for shifted complexes, first proved
by Klivans and the first and fourth authors. In each case, we add facets one at
a time, and give explicit expressions for simplicial effective resistances of
added facets by constructing high-dimensional analogues of currents and
voltages (respectively homological cycles and cohomological cocycles).
