# Homework Help: Capacitance on cubic circuit

1. Nov 28, 2012

### V0ODO0CH1LD

1. The problem statement, all variables and given/known data

A potential electrostatic difference is stablished between points M and Q in the cubic circuit of identical capacitors shown in the image. What is the potential difference between points N and P?

2. Relevant equations

3. The attempt at a solution

I tried opening up the cube to make it look like something that I am used to, but it still looked confusing.

#### Attached Files:

• ###### Untitled.jpg
File size:
16.4 KB
Views:
57
2. Nov 28, 2012

### Staff: Mentor

There are two unnamed points equivalent to N, and two unnamed points equivalent to P. You can add (imaginary) connections between them, this allows to draw a simple, equivalent planar diagram.

3. Nov 28, 2012

### V0ODO0CH1LD

Would it be correct to assume that whatever current I have flowing into M it gets split up in three? And then in two at the next node? Reuniting at the end to deliver the same current to node Q?

I tried to draw an equivalent diagram, but I can't get it to look right.. I think there's something I am missing.

4. Nov 28, 2012

### Staff: Mentor

Right. And you can draw this as planar graph as well.

5. Nov 28, 2012

### V0ODO0CH1LD

I struggled a lot with it.. Than I came across this article that explained a similar problem but with resistors!

In the article, it said that since the first three nodes from the source of potential difference have the same current going though them. I can assume they are somehow equivalent points. And by using the same assumptions with the remaining nodes you can arrive at a schematic where you have two sets of three capacitors in parallel in series with six capacitors in parallel. Like M--(3 parallel)---(6 parallel)---(3 parallel)--Q.

The thing is, I don't get how you could arrive at this. How can I just say that those three first nodes could be represented by one?

Also trying to flatten the cube will get you nowhere. I tried all possibilities.. Either you have to understand the assumption above or I am really missing something. Because I just couldn't do it..

6. Nov 28, 2012

### ehild

The problem of cube of resistors was discussed in Physicsforums several times. Try to follow this thread: https://www.physicsforums.com/showthread.php?t=557461

The method of solution is based on symmetry. (See the thread from Post #6) Equivalent points are at the same potential. Points on same potential can be connected with a wire, it changes nothing in the electric circuit. The points connected with a wire of zero resistance represent a single node.

ehild

7. Nov 29, 2012

### V0ODO0CH1LD

Thanks! I was also wondering something else: is the voltage across the whole cube the same? If I measured the electric potential difference between any two points will they all give back the same value? Because I was thinking; if I measured the voltage from point M to point N and from point N to point P, they would differ. Because I have the same resistance but half the current, and by Ohm's law V = IR, the voltage of between M and N would be twice the voltage between N and P. Is that correct?

8. Nov 29, 2012

### ehild

I drew the equivalent points by coloured dots. The voltage is the same between identical pairs: between the black dot and the red ones, (that is between M and N , M and K, M and L). It is the same also between the blue ones and the orange one: PQ, RQ, SQ. But it is different for the other pairs.
The voltage between M and N is not the same as the voltage between N and P. It is a bit easier to follow the potential of the nods. M is at zero potential and Q is at V potential. The potential increases with the same amount from M to N, from M to K and from M to L, and the same is the increase from P to Q, from R to Q and from S to Q. But you get different change of potential from N to P, N -->R, L-->S, L-->P, K-->R, K-->S.

ehild

#### Attached Files:

• ###### capcube.JPG
File size:
20.2 KB
Views:
56
9. Nov 29, 2012

### V0ODO0CH1LD

Okay, but I am still confused as to why the potential difference is different from:
N --> P, N -->R, L-->S, L-->P, K-->R, K-->S.

If I had three amperes flowing into M. Would't that current split into three currents of one ampere each flowing towards N, L and K? Then at those nodes they would split yet again into two currents of 1/2 ampere? So that you would have flowing into P 1/2 A from N and 1/2 A from L? And into S; 1/2 A from K and 1/2 A from L?

10. Nov 29, 2012

### CWatters

I think you missunderstood what he said. He meant...

Vblack to Vred = Vblue to orange <> Vred to Vblue

There are three caps between black and red and between blue and orange but six caps between red and blue.

11. Nov 29, 2012

### ehild

These are all equal, but different from VMN (half of it).

ehild