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So,from the very first of my current electricity classes,I got to know these 2 things

1)Current flows from higher to lower potential

Which means current flows between two points if only there is a potential difference between them,right? But in this example,

enter image description here

current flows through the wire AB even though the potential difference is 0.

But A and B are the same node.I remember my teachers told that we can remove anything between same nodes.But why can't we remove the wire AB here?Why does it make the circuit different

Again,let's take the example of a balanced wheatstone bridge.Current doesn't flow through the middle wire.They have the same nodes across them.Our teacher told we can add an wire across the nodes to make the calculations easier.

So what is the difference between 1st and 2nd case?Why can't we remove the wire in the 1st example?

Qmechanic
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aiman
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2 Answers2

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Which means current flows between two points if only there is a potential difference between them, right?

Wrong.

The potential difference between two points is the work required per unit charge to move the charge between the two points. A zero resistance wire between two points theoretically requires no work to move charge (current) between the two points. So in theory you can have current between two points with a zero potential difference.

The thing is, with the exception super conductors, all real conductors (wires) have some resistance. Thus, with the exception of superconductors, there will be a potential difference between two points of any conductor where current flows.

With regard to wires shown in circuit diagrams, unless otherwise specified, it is assumed that their resistance is negligible compared to the resistance of the resistors shown in the circuit. So your teacher is correct that a wire can technically be "shrunk" to a point (node). Think of the wires in diagrams as a convenience to make it easier to visualize the currents in a circuit.

Hope this helps.

p.s. One apparently needs a google account to access your link.

Bob D
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  • What about the wheatstone bridge?The current doesn't flow through the middle resistor because the potential difference across the resistor is 0.Which means we can remove the resistor and add a wire there,right?But then would current flow through that wire? – aiman Dec 17 '23 at 13:30
  • What middle resistor? The Wheatstone bridge doesn't have a middle resistor. It has a galvanometer which measures current. When it reads zero the current is zero and the bridge is "balanced". – Bob D Dec 17 '23 at 16:24
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Have a look at the circuits below with the connection between the two middle nodes being changed from open circuit, a $10\Omega$ resistor and short circuit.

enter image description here

On the right hand side is a balanced Wheatstone bridge with the nature of the connection between the middle two nodes not influencing the rest of the circuit.

On the left hand side the arrangement is not a balanced Wheatstone bridge and the nature of the connection between the middle two nodes does influence the rest of the circuit.

Also remember that the connecting wires are assumed to have zero resistance so although they carry a current there is no potential difference across them.
If the connecting wires did have a resistance which was significant relative to other resistors in the circuit then that resistance would have to be included in any analysis of the circuit.

Farcher
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  • Yeah I understand it but our teacher told we can remove anything between two same nodes.Why doesn't it apply to the 3rd case of the unbalanced wheatstone bridge? – aiman Dec 17 '23 at 14:38
  • Because there is a current running through the connecting wire. – Farcher Dec 17 '23 at 16:00