Why Does No Current Flow Between C and D in This Circuit?

[Kara386]

In the circuit in the image attached, why does no current flow between C and D? I've been told it's a short circuit I just don't see why, there is a resistor in that branch. The source is connected between terminals A and B.

 

[Khashishi]

Your problem is underspecified. Where are the sources? What are the resistances?

 

[Kara386]

Your problem is underspecified. Where are the sources? What are the resistances?

Oh sorry! The source is connected between terminals A and B, which I took to mean in parallel across A and B although now I think about it that may not be what it means. Resistances are 10 ohms each. The problem is easy to solve once you know that no current flows between C and D, but I find it hard to see why no current flows there.

 

[Khashishi]

In general, there could be current. But, are the resistors all the same?

 

[Kara386]

In general, there could be current. But, are the resistors all the same?

Yes, identical. We were told to use the symmetry of the problem to solve it.

 

[Khashishi]

Well, what do you think symmetry tells you?

 

[Kara386]

Well, what do you think symmetry tells you?

I have no idea why symmetry would prevent current flowing between C and D. All I've ever been told about short circuits is you find them by finding a path from the positive to negative terminal that avoids going through any load.

 

[Khashishi]

What does symmetry tell you about the voltages in the nodes?

 

[protoslash]

- assume point A is connected to the positive source, and point B is connected to the negative source. Assume AB potential is V
- assume all resistance is the same
- do KVL around ADB loop. DB will have potential V/2
- do KVL around ACB loop. CB will have potential V/2 as well.
- Therefore with respect to B, Two points C and D have the same voltage potential, so no currents flow from C to D

I don't think you can call C-D short circuit since there is resistance between the two point. It just works out that the C and D have the same potential so no currents will flow.

 

[cnh1995]

I have no idea why symmetry would prevent current flowing between C and D. All I've ever been told about short circuits is you find them by finding a path from the positive to negative terminal that avoids going through any load.

You can use Thevenin's theorem here. Remove the resistance in branch CD and find the Thevenin voltage V_cd. It will be zero.

You'll need to use KVL for the two loops as @protoslash said in the previous post.

 

[Kara386]

- assume point A is connected to the positive source, and point B is connected to the negative source. Assume AB potential is V
- assume all resistance is the same
- do KVL around ADB loop. DB will have potential V/2
- do KVL around ACB loop. CB will have potential V/2 as well.
- Therefore with respect to B, Two points C and D have the same voltage potential, so no currents flow from C to D

I don't think you can call C-D short circuit since there is resistance between the two point. It just works out that the C and D have the same potential so no currents will flow.

Ah, that would lead to a sort of general principle that current doesn't cross a line of symmetry then. Doesn't flow from one side to the other. Thanks!

 

[nasu]

And in general, a short circuit between two points does not mean that there is no current but quite the opposite.

 

[CWatters]

Ah, that would lead to a sort of general principle that current doesn't cross a line of symmetry then. Doesn't flow from one side to the other. Thanks!

Its more than that...

If two nodes are at exactly the same voltage then you can short them together or open circuit them without affecting the circuit. That can make it a lot easier analyse.

 

[Bassam Salman]

Hi
because the deferential voltage on D and C will be zero (equivalent circuit from A to D and B equal to A to C and B)