  Consider a rooted infinite Galton-Watson tree with mean offspring number
$m>1$, and a collection of i.i.d. positive random variables $\xi_e$ indexed by
all the edges in the tree. We assign the resistance $m^d \xi_e$ to each edge
$e$ at distance $d$ from the root. In this random electric network, we study
the asymptotic behavior of the effective resistance and conductance between the
root and the vertices at depth $n$. Our results generalize an existing work of
Addario-Berry, Broutin and Lugosi on the binary tree to random branching
networks.
