How Does Point Connection Affect Potential in a Circuit with Resistor Ratios?

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Homework Help Overview

The discussion revolves around an electric circuit involving resistors R1 and R2, specifically focusing on how the connection of points M and N, which have the same electric potential, affects the overall potential in the circuit. The relationship between the resistors is given as R1 = √2.R2.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the implications of connecting points M and N, questioning how this affects the potential at those points and the overall circuit behavior. There are discussions about symmetry in the circuit and the potential differences created by removing certain resistors.

Discussion Status

Participants are actively questioning the assumptions about the potentials at points M, N, and O, with some suggesting that symmetry might play a role. There is a recognition that the resistances along different paths affect the potentials, but no consensus has been reached on the implications of these observations.

Contextual Notes

There is an ongoing examination of the assumptions regarding the equal potentials at points M and N, as well as the effects of resistor configurations on these potentials. The discussion is constrained by the need to adhere to homework guidelines, which may limit the depth of exploration.

Peter Velkov
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Given an electric circuit, with resistors R1 and R2, find the equivalent resistance R.
Data: R1 = √2.R2

Points M and N have the same electric potential so they can be connected with a conductor and this way we get the second circuit.
222.png
 
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Peter Velkov said:
Points M and N have the same electric potential so they can be connected with a conductor and this way we get the second circuit.
There is more you can do to simplify the circuit.
 
In terms of what? I know i can solve the parallel ones below, however that won't solve it. There should be a way to proof that M and N are also equal to O.
 
Sure, use symmetry again.
 
mfb said:
Sure, use symmetry again.
It's symmetrical along MO, NO but that doesn't help us much.
 
Temporarily remove the two vertical R2's. What are the potentials at M,N,O?
 
gneill said:
Temporarily remove the two vertical R2's. What are the potentials at M,N,O?
On the upper side we will have a resistor with √2R2, but on the down side R2/√2. So they will be different.
 
Peter Velkov said:
On the upper side we will have a resistor with √2R2, but on the down side R2/√2. So they will be different.
Really? What was your argument for M and N having the same potential in your first post?
 
gneill said:
Really? What was your argument for M and N having the same potential in your first post?
Equal amounts of charge will flow through the upper or downer R1, and since the resistance is equal the voltage will be too. However I don't understand why the points O and M or N will have the same potential as the resistance along the path is different.
 
  • #10
Peter Velkov said:
Equal amounts of charge will flow through the upper or downer R1, and since the resistance is equal the voltage will be too. However I don't understand why the points O and M or N will have the same potential as the resistance along the path is different.

The potentials at M,N, and O are due to the voltage dividers comprised of the resistances in their branches. Here's the situation:
Fig1.png

All three branches have the same potential difference across them (whatever you imagine to be placed across terminals AB). All three branches have the same resistance ratios...
 

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