Which pairs of these diagrams represent equivalent circuits?

[syllll_213]

Homework Statement

Circuit

Relevant Equations

I(in) = I (out)

Hi, I came across this question and I wonder if my option is correct? I was thinking in Y and Z the current both divide (Kirchoff's Current Law) so they should be the same, while in X the current does not seem to divide and in Y I am struggling to visualise the division or current flow...

 

[.Scott]

You get to pick more than one of the choices (and you should).

 

[Gavran]

In circuit diagrams, connections are ideal wires with zero resistance, so a node consists of the entire section of wire between elements, not just a single point. (https://en.wikipedia.org/wiki/Node_(circuits))

 

[kuruman]

I think that, instead of considering Kirchhoff's current law, it would be easier to see what's going on if you considered the voltage law and that straight lines in circuit depiction represent equipotentials regardless of their shape. You can see that in all four diagrams one side of elements A-D is at the same potential. In W and Z the other side of A is at the same potential as the other side of B and the other side of C is at the same potential as the other side as D. Thus, as you have correctly concluded, W and Z are equivalent.

Now apply the same reasoning to X and Y.

 

[Steve4Physics]

I was thinking in Y and Z the current both divide (Kirchoff's Current Law) so they should be the same

You could start with the 'easy' feature: Y has four external connections but Z has only two. So can they be equivalent?

Here's an exercise for you. There is a 'black box' with four terminals:

The only components inside the black box are 4 perfectly conducting wires connected like this:

Which (zero, one or more) of the following circuits (also made of perfectly conducting wires) is/are equivalent to the above circuit?
(By ‘equivalent’ we mean that we can’t tell which circuit is inside the black box – equivalent circuits behave the same as each other.)