  We discuss several parametrizations of the space of circular planar
electrical networks. For any circular planar network we associate a canonical
minimal network with the same response matrix, called a "standard" network. The
conductances of edges in a standard network can be computed as a biratio of
Pfaffians constructed from the response matrix. The conductances serve as
coordinates that are compatible with the cell structure of circular planar
networks in the sense that one conductance degenerates to 0 or infinity when
moving from a cell to a boundary cell. We also show how to test if a network
with n nodes is well-connected by checking that $\binom{n}{2}$ minors of the
$n\times n$ response matrix are positive; Colin de Verdi\`ere had previously
shown that it was sufficient to check the positivity of exponentially many
minors. For standard networks with m edges, positivity of the conductances can
be tested by checking the positivity of m+1 Pfaffians.
