- #1
General solution to the circuits
- Thread starter killingb
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Discussion Overview
The discussion centers around finding a general solution for a circuit involving a ladder network of resistors, specifically focusing on the behavior of the equivalent resistance as the number of resistors approaches infinity. The scope includes theoretical considerations and mathematical reasoning related to circuit analysis.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant proposes that if the circuit leads to an infinite but converging series, and with resistors R1, R3, and R5 in increasing magnitude while R2 remains constant, there may be a general formula applicable to the problem.
- Another participant suggests that the equivalent resistance of the ladder network can be expressed as R2 in parallel with the rest of the ladder, implying that R2 could be the solution under certain conditions.
- A different participant questions the clarity of the original question and provides insights into the limits of measured resistance in the circuit, indicating that the resistance measured at specific points will have upper and lower bounds based on the resistances involved.
- There is a mention of the current through certain resistors approaching zero, which raises questions about the implications of infinite resistors in the network.
Areas of Agreement / Disagreement
Participants express differing views on the nature of the circuit and the implications of infinite resistors, indicating that multiple competing perspectives remain without a clear consensus on the general solution.
Contextual Notes
There are limitations in the clarity of the original question and the assumptions regarding the circuit configuration, as well as the dependence on the definitions of the resistances involved.
Who May Find This Useful
This discussion may be of interest to those studying circuit theory, particularly in the context of infinite resistor networks and their equivalent resistances.
- #2
Danger
Gold Member
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Not that I could help you with your question anyhow, but it might be a good idea for you to re-post your diagram. I can't even see the lettering on it.
- #3
SGT
The equivalent resistance of the ladder network is [tex]R_2[/tex] in parallel with the rest of the ladder (from [tex]R_1[/tex] to infinity).
If I understood it well, [tex]R_2[/tex] is the solution. For the resistance of a parallel connection to be equal to one of the resistances, the other one must be infinity.
If I understood it well, [tex]R_2[/tex] is the solution. For the resistance of a parallel connection to be equal to one of the resistances, the other one must be infinity.
- #4
Danger
Gold Member
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My apologies, killingb... I didn't realize until now that the picture was enlargeable after opening. 
Last edited:
- #5
NoTime
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I'm not sure what the question is.
If you lable the left input as A B and the right output as C D.
Then the measured resistance A B will never be greater than R_2,1 or less than sqrt(R_2,1^2 + R_1^2).
The measured resistance at C D will never be > R_n + R_2,n or < R_n.
The measured current through R_2,n will approach 0.
Where does the infinity come from?
If you lable the left input as A B and the right output as C D.
Then the measured resistance A B will never be greater than R_2,1 or less than sqrt(R_2,1^2 + R_1^2).
The measured resistance at C D will never be > R_n + R_2,n or < R_n.
The measured current through R_2,n will approach 0.
Where does the infinity come from?
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