Will any charge flow through the circuit?

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SUMMARY

The discussion centers on the flow of charge in a circuit with zero resistance wires and the implications for current flow. Participants clarify that while the potential difference across ideal wires is zero, current can still flow through them due to their negligible resistance. The equivalent resistance of the circuit is calculated as 2r/5, and it is established that current will divide among all available paths, including those with zero resistance, as long as there is a potential difference driving the flow.

PREREQUISITES
  • Understanding of basic circuit theory, including Ohm's Law (V=IR).
  • Familiarity with concepts of open circuits and short circuits.
  • Knowledge of parallel and series circuit configurations.
  • Ability to apply Kirchhoff's laws for circuit analysis.
NEXT STEPS
  • Study the principles of current division in parallel circuits.
  • Learn about the implications of superconductors and their zero resistance properties.
  • Explore circuit simplification techniques, including node analysis.
  • Investigate the effects of resistive and non-resistive paths in circuit design.
USEFUL FOR

Electrical engineering students, circuit designers, and anyone interested in understanding current flow in electrical circuits, particularly in scenarios involving zero resistance paths.

  • #31
Your "short circuits" are simply wires connecting components. There's nothing special about these wire connections. Neither of them are in parallel with any components in the strict definition of "parallel connection". Geometric layout on a drawing does not make things parallel; It's the connection topology that counts.

Contiguous wire pathways on a circuit diagram comprise nodes. It's the connections of components between nodes that define the circuit topology. You can stretch or bend or otherwise contort the drawing of these nodes in any fashion you like so long as you don't change what connects to them (components). You can move any connection to a given node to any location on the same node without changing the circuit topology.

You need to practice "morphing" circuit diagrams by bending or stretching node wires, or "sliding" connections along a node to make the circuit more easy to comprehend. With a bit of experience this will become much easier, and you'll wonder what all the fuss was about.

You should be able to follow three distinct paths from A to B on your original diagram. By distinct I mean that they each pass uniquely through a subset of the components, never passing through the same component twice or passing though a component that is covered by another path. Wires do not count as components: you are allowed to use the same wire for multiple paths. Those three distinct paths will be three parallel branches (in the strict definition of parallel connection) that connect node A to node B.
 
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  • #32
circuit.jpg


You don't seem to get that 1 and 3 are the same thing and then 4 and 2 are the same thing. You did not do what I suggested and follow ALL the lines and figure out which of the original are which in the modified circuit.
 
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  • #33
Yes, I also don't see a mistake in @phinds 's redrawing of the circuit. It's just the topology that matters here!
 
  • #34
:oldcry: Was my post #6 totally in vain ?
 
  • #35
BvU said:
:oldcry: Was my post #6 totally in vain ?
Both of our efforts were long in vain. Maybe he gets it now.
 
  • #36
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  • #37
donaldparida said:
@phinds I got it.
Excellent. It's a common problem w/ people who are new to circuits and once you get it, it just isn't a problem any more (as long as you remember to apply it :smile: )
 

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