# Which of these diagrams represent the same circuit?

## Homework Statement

Which of these diagrams represent the same circuit?

## The Attempt at a Solution

I thought it was A and D because it seems to me that in both cases the current is going splitting into two different paths. Also it seems to me that in A and D the potential difference is the same.

But that's incorrect and I can't understand why.

A and B seems wrong to me because the capacitor is at a different potential.
A and C seems wrong because the resistor blocks the capacitor in C.
B and C seems incorrect because of the resistor blocking the capacitor in C but not in B.
B and D seems incorrect because the capacitor at B looks like it is at a higher potential.

Basically I've ruled out C. The resistor that blocks the battery makes it unique.

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Matterwave
Gold Member
I think you are correct in ruling out C. A simple way to see that is the capacitor has been short circuited by the straight wire to its left! No current will ever flow to the capacitor since the current can choose a path with 0 resistance.

I also think your conclusion that A and D are equivalent is correct. But I don't understand why you ruled out B. Why do you think the capacitor is at higher potential? Let's look at the capacitor portion of the circuit. If I draw --||--------------------- is this different than --------------||-------------? Does the length of my (0 resistance) wires matter?

Answer A and D was incorrect but I don't understand why.

I thought that it was at a higher potential because at A the capacitor is parallel with the battery while at B it isn't.

phinds
Gold Member
2019 Award
Can you redraw A, B, and D so that they look the same (without, of course, changing anything at any of the nodes) ?

A and B should work. But as I said, it's not the correct answer.

Matterwave
Gold Member
A and B should work. But as I said, it's not the correct answer.
Are you given multiple choice for this problem, or are you asked to provide your own answer?

Also, you seem to think that the capacitor in B is not in parallel with the other circuit elements, why do you think this?

Multiple choice.

And I just noticed that there was an A, B and D choice at the end of the table, and that was correct. Duh.

I thought B was at a different potential because it's not at the same "height" as the battery.

Matterwave
Gold Member
Does height on a circuit diagram matter? What if I flipped the diagram up-side-down, would you say it's at a lower potential then?

Seems like it doesn't, which clears up a lot of what was confusing me about them. My professor has an outrageous accent and I have a very hard time understanding him. He was talking about how we should treat circuit diagrams as "gravitational potential energy" but I couldn't really understand much more of what he said.

So if I understood this correctly, I select a point where V=0 then go around the circuit and when I get back to that point the sum of all the changes = 0 (Kirkhoff's law)?

Matterwave
Gold Member
Yes, you can start at the bottom left in B, go past the battery and get V go to the top right and pass by the capacitor and you have to get -V from the capacitor so you end up with 0 when you finish the loop. In diagram A you do the same and find that the capacitor also has voltage -V. As long as you don't move past a node, or past another circuit element, you are free to move circuit elements around. Because making a longer or shorter wire does not matter to the circuit since wires are assumed to be resistance-free.

So in diagram B, I can just move to capacitor from being on the top right to the right edge (no node or other circuit element was passed) and you can clearly see that it's the same as A.

CWatters