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.

 

[Nickie]

I can confirm that the statement about the limited options for topologies in a two terminal electrical device is correct. This is due to the fundamental laws of circuit analysis, specifically Kirchhoff's laws, which dictate that in a two terminal device, the net current entering one terminal must be equal to the net current exiting the other terminal. This means that all elements in the circuit must be connected in a series or parallel configuration in order for the circuit to function properly.

In a series connection, the elements are connected one after the other, with the same current flowing through each element. This is the simplest and most common topology in a two terminal device. In a parallel connection, the elements are connected side by side, with the same voltage applied to each element. This allows for different currents to flow through each element.

Other topologies, such as a delta or wye configuration, require more than two terminals and are not possible in a two terminal device. These topologies are commonly used in three-phase power systems, where there are three terminals.

In summary, the limited options for topologies in a two terminal device are a result of the fundamental laws of circuit analysis and the need for a series or parallel configuration for proper functioning.