Assume V(t), I(t), ε(t) are all proportional to exp(iωt).

Assume idealized circuit elements.  Define the impedance Z = V/I.  Then

Kirchhoff’s rules for filamentary circuits:

For each loop   for each node   

Any two-terminal network of passive elements is equivalent to an effective impedance Z_eff.

Thévenin equivalent circuits: Any two terminal network can be replaced by a generator ε_eff in series with an impedance Z_eff.

Norton equivalent circuits: Any two terminal network can be replaced by a current source I_eff in parallel with an impedance Z_eff.

Power:

P_avg = (1/2)Re(VI*) = I²_rmsR.  The maximum power is delivered to a load when Z_load = Z_eff^*.

Ladder networks:

Consider an infinite ladder network of elements, for example the network shown below.

The network is equivalent to a network terminated by Z₀, if    

.

If Z₀ is real the circuit absorbs energy, if  Z₀ is imaginary, it does not absorb energy.  If Z₀ is real signals can pass to the load, if Z₀ is imaginary, signals cannot pass to the load, we have a filter.