  We study a model of random electric networks with Bernoulli resistances. In
the case of the lattice Z^2, we show that the point-to-point effective
resistance between 0 and a vertex v has a variance of order at most (log
  |v|)^(2/3) whereas its expected value is of order log |v|, when v goes to
infinity. When the dimension of Z^d is different than 2, expectation and
variance are of the same order. Similar results are obtained in the context of
p-resistance. The proofs rely on a modified Poincare inequality due to Falik
and Samorodnitsky.
