  We give lower bounds for the electrical resistance between vertices in the
Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2)
mother groups on the orbit of the zero ray. These bounds, combined with results
of \cite{JNS} show that every quadratic activity automaton group is amenable.
The resistance bounds use an apparently new "weighted" version of the
Nash-Williams criterion which may be of independent interest.
