No Current Between AF & DG in Symmetrical Circuit: True?

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In summary, due to the symmetry of the circuit, there is no current between the junctions (AF) and (DG) and they have the same potential. This is because both branches of the circuit have equal resistances on either side, resulting in equal potential at AF and DG. This eliminates the need for top-bottom symmetry to eliminate current between the two junctions.
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Due to the symmetry of the circuit there is no current through the resistor between the junctions (AF) and (DG) so the junctions (AF) and (DG) have the same potential.

I don't understand how this is true. The circuit is symmetrical left-right but not top-bottom. Isn't top-bottom symmetry what is required to eliminate current between AF and DG?
Thanks!
 
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  • #2
Hi sparkle123! :smile:

Due to the horizontal symmetry, all points in the circuit that are on the vertical center line have the same potential.
(There's as much resistance left as right of these points.)

When there is no potential difference, no current will flow.
 
  • #3
The top branch with R1 and R1 leaves the AF junction half way between the potentials at E and B.

The bottom branch also has equal resistance on either side, splitting the potential to half way between E and B. The potentials at AF and DG are the same so there is no current from one to the other.

edit: didn't see your post before posting, I like Serena.
Great minds think alike?
 
  • #4
Thanks I like Serena and Delphi51! :)
(yes, great minds do think alike!)
 
  • #5


I would like to clarify that the statement is indeed true. The symmetry of the circuit refers to its left-right symmetry, which means that the circuit is identical when flipped horizontally. This symmetry ensures that the current flowing through the resistor between junctions (AF) and (DG) is equal in both directions, resulting in a cancellation of current and thus no net current between the two junctions. The top-bottom symmetry is not necessary for this phenomenon to occur. I hope this clarifies any confusion.
 

1. What does it mean when there is no current between AF and DG in a symmetrical circuit?

When there is no current between AF and DG in a symmetrical circuit, it means that the circuit is balanced and there is equal resistance on both sides. This results in no potential difference between the two points, causing no current to flow.

2. Is it possible for there to be no current between AF and DG in a symmetrical circuit?

Yes, it is possible for there to be no current between AF and DG in a symmetrical circuit. This can occur when the circuit is balanced and there is equal resistance on both sides, resulting in no potential difference and no current flow.

3. Can a symmetrical circuit have unequal resistance on both sides and still have no current between AF and DG?

No, in a symmetrical circuit, if there is unequal resistance on both sides, there will be a potential difference between the two points. This will cause current to flow, breaking the symmetry of the circuit.

4. How does the absence of current between AF and DG affect the overall circuit?

The absence of current between AF and DG in a symmetrical circuit does not affect the overall circuit as long as the circuit remains balanced. This means that the total current in the circuit will still be the same, with the only difference being that there is no current flowing between these two points.

5. Can the absence of current between AF and DG impact the accuracy of calculations in the circuit?

No, the absence of current between AF and DG does not impact the accuracy of calculations in the circuit as long as the circuit remains balanced. However, if there is a slight imbalance in the circuit, it can affect the accuracy of calculations as it may result in a small amount of current flowing between these two points.

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