General topology of a two terminal electrical device

[tarjeibo]

There are several possible topologies for an electrical circuit.

However, if we limit our circuit to be a two terminal device, how will this limit the options for the different topologies?

I am a beginner in this field, but as far as I can tell by drawing the circuits, the only possible topologies in a two terminal device are the well-known series and parallel connections. Is this true, and if yes, why is that? If not, what other types of topologies are possible to construct in a two-terminal device?


Thanks,
Tarjei

 

[haruspex]

Not sure I've understood the question, but what about making all six possible connections between four nodes, then attaching nodes to two them?

 

[tarjeibo]

I will try to rephrase my question.

Given a two terminal device. Between the two terminals, we may have as many resistors, capacitors and inductors as we want. My question is then:

Is the only possible topology between the two terminals series and parallel connection. Or is it possible to "create" other, more complex topologies as well, given that we only have two terminals?

 

[haruspex]

I will try to rephrase my question.

Given a two terminal device. Between the two terminals, we may have as many resistors, capacitors and inductors as we want. My question is then:

Is the only possible topology between the two terminals series and parallel connection. Or is it possible to "create" other, more complex topologies as well, given that we only have two terminals?

How are you defining 'terminal'? I think of a network as consisting of nodes and links. (Vertices and edges, in graph theory terminology.) Are you calling every node a terminal, or only those nodes that have a single link?
If every node is a terminal then you only have two nodes, and the only circuits possible are parallel.
If only nodes of degree one are terminals then you can use the construction I posted before, which cannot be reduced by successive grouping into parallel and series clusters.