  Let $G=(V,E)$ be a random electronic network with the boundary vertices which
is obtained by assigning a resistance of each edge in a random graph in
$\mathbb{G}(n,p)$ and the voltages on the boundary vertices. In this paper, we
prove that the potential distribution of all vertices of $G$ except for the
boundary vertices are very close to a constant with high probability for
$p=\frac{c\ln n}{n}$ and $c>1$.
