  In this paper, we study 2-port networks and introduce new concepts of voltage
drop and $\Pi$-equivalence. The main result is that each planar network is
$\Pi$-equivalent to a network with no more than 5 edges. This implies that if
an octagon in the shape of the letter $\Pi$ can be tiled by squares then it can
be tiled by no more than 5 rectangles with rational aspect ratios. Kenyon's
theorem from 1998 proves this only for 6 rectangles.
