  Consider an electrical circuit $G$ each directed edge $e$ of which is a
semiconductor with a monomial conductance function $y_e^* = f_e(y_e) = y_e^s /
\mu_e^r$ if $y_e \geq 0$ and $y_e^* = 0$ if $y_e \leq 0$. Here $e$ is a
directed edge, $y_e$ is the potential difference (voltage), $y_e^*$ is the
current in $e$, and $\mu_e$ is the resistance of $e$; furthermore, $r$ and $s$
are two strictly positive real parameters common for all edges. In particular,
case $r = s = 1$ corresponds to the Ohm law, while $r = \frac{1}{2}, s =1$ may
be interpreted as the square law of resistance typical for hydraulics and gas
dynamics. We will show that for every ordered pair of nodes $a, b$ of the
circuit, the effective resistance $\mu_{a,b}$ is well-defined. In other words,
any two-pole network with poles $a$ and $b$ can be effectively replaced by two
oppositely directed edges, from $a$ to $b$ of resistance $\mu_{a,b}$ and from
$b$ to $a$ of resistance $\mu_{b,a}$. Furthermore, for every three nodes $a, b,
c$ the inequality $\mu_{a,c}^{s/r} + \mu_{c,b}^{s/r} \geq \mu_{a,b}^{s/r}$
holds, in which the equality is achieved if and only if every directed path
from $a$ to $b$ contains $c$. MSC classes: 11J83, 90C25, 94C15,94C99
