  In this paper we deal with the notion of the effective impedance of AC
networks consisting of resistances, coils and capacitors. Mathematically such a
network is a locally finite graph whose edges are endowed with complex-valued
weights depending on a complex parameter $\lambda $ (by the physical meaning,
$\lambda =i\omega $, where $\omega $ is the frequency of the AC). For finite
networks, we prove some estimates of the effective impedance. Using these
estimates, we show that, for infinite networks, the sequence of impedances of
finite graph approximations converges in certain domains in $\mathbb{C}$ to a
holomorphic function of $\lambda$, which allows us to define the effective
impedance of the infinite network.
