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We calculate effective impedances of infinite $LC$- and $CL$- ladder networksas limits of effective impedances of finite network approximations, using a newmethod, which involves precise mathematical concepts. These concepts arerelated to the classical differential operators on weighted graphs. As anauxiliary result, we solve a discrete boundary value Dirichlet problem on afinite ladder network.

The effective impedances of infinite ladder networks and Dirichlet problem on graphs