Combined resistance in this circuit

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Homework Help Overview

The discussion revolves around calculating the combined resistance in a circuit after a switch is closed, with participants exploring various methods and approaches to arrive at the answer.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss applying Kirchhoff’s law and express uncertainty about the efficiency of their methods. Some attempt to use spreadsheet calculations to estimate currents and voltages, while others question the accuracy of the provided answer of 4Ω.

Discussion Status

The conversation is ongoing, with participants sharing their individual approaches and questioning the results. There is mention of alternative methods, such as delta/Y transforms, which some participants suggest could be more efficient.

Contextual Notes

Some participants express confusion regarding the measurements and calculations, noting potential rounding issues and the need for clarification on the methods used to derive the resistance values.

Eitan Levy
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Homework Statement


Find the combined resistance once the switch is closed.

Homework Equations


V=IR

The Attempt at a Solution


I tried applying Kirchoff’s law but I got many equations, I am sure there is a more efficient way. I also tried to re-draw the circuit, but wasn't sure how to do so. The answer is 4Ω.
 

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The resistance is measured from top to bottom.
I do not get exactly 4.

I used a spread sheet.
I took node C as the top and D as the bottom, and assumed the current through the network was 1.
Then I set current CA to an estimated value and deduced all other currents (CB, AB, BD, and AD) based on that. Then, given the resistances, I computed all 5 of those voltages. Then I computed the total voltages CA+AB+BD and CB-AB+AD. Then I adjusted my original estimate for CA current to make those two total voltages equal.

That's probably as awkward as any other method. But it gave me an answer.
 
Last edited:
.Scott said:
The resistance is measured from top to bottom.
I do not get exactly 4.
Perhaps it was rounded. Could you explain how you got it?
 
Eitan Levy said:
Perhaps it was rounded. Could you explain how you got it?
I just edited post #2 with details.
If you're handy with Excel (or other spread sheet), it is pretty straight forward.
 
Eitan Levy said:
Could you explain how you got it?
Resistors28628.png


Cells F18:21 are copies of F17.
Cells H23:J23 are copies of G23

All 4 values on row 22 should be the total voltage (and therefore impedance) from top (node C) to bottom (node D)

The 0.023 factor in line 25 results from experimentation. I did a few E23 adjustments manually until I saw what the approximate correction factor was. Then I put that into the "Improved Estimate" calculation.
 

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Eitan Levy said:
I am sure there is a more efficient way.
check out delta / Y transforms (or in your case, Y / delta transforms)
 
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