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

AI Thread Summary
In the discussion on how point connection affects potential in a circuit with resistor ratios, the focus is on finding the equivalent resistance R for resistors R1 and R2, where R1 equals √2 times R2. Points M and N can be connected due to having the same electric potential, leading to a second circuit configuration. The conversation explores the symmetry in the circuit and the implications of removing certain resistors to analyze potential differences at points M, N, and O. It is noted that while equal charge flows through resistors, the differing resistances along paths can lead to confusion regarding potential equality. Ultimately, the potentials at M, N, and O are determined by the voltage dividers formed by the resistances in their respective branches.
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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