Resistance of this circuit containing a Circular section

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Homework Help Overview

The discussion revolves around calculating the resistance in a circuit that includes a circular section and involves multiple resistors arranged in series and parallel configurations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning how certain resistances are derived, particularly the transition from R to 1Ω and the calculation of total resistance for resistors in parallel. There is also a focus on understanding the configuration of the circuit and the implications of the circular section.

Discussion Status

The discussion is ongoing, with participants actively engaging in clarifying their understanding of the circuit's layout and resistance calculations. Some have provided guidance on calculating total resistance for parallel resistors, while others express difficulty in visualizing the circuit setup.

Contextual Notes

Participants mention challenges in picturing the circuit configuration and the corresponding lumped model, indicating a potential gap in visual representation or understanding of the problem setup.

Aristarchus_
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Homework Statement
A piece of wire has resistance R. The wire is cut into three parts of equal length and connected
together as shown in the figure. What will be the resistance between A and B?
Relevant Equations
Solution is 1/12 + 2/3 = 3/4ohm.
1659873059820.png

I understand that the two separate parts make 2/3, but where is 1/12 ohm coming from?
 
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How did R turn into ##1\Omega##?
Call the two points where the straight sections meet the circle C, D. There are two parallel paths (electrically speaking) from C to D. What is the resistance of each?
 
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haruspex said:
How did R turn into ##1\Omega##?
Call the two points where the straight sections meet the circle C, D. There are two parallel paths (electrically speaking) from C to D. What is the resistance of each?
1659873869220.png

But would we calculate then resitance in parallel(1/6 and 1/6)?
 
Yes exactly, what total resistance you get if you connect two resistors of 1/6 in parallel?
 
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Delta2 said:
Yes exactly, what total resistance you get if you connect two resistors of 1/6 in parallel?
right! Hmm... However, it is hard to picture the circuit in the way you described it. I could not come up with that sketch on my own...
 
Aristarchus_ said:
right! Hmm... However, it is hard to picture the circuit in the way you described it. I could not come up with that sketch on my own...
Yes agreed from the image of the wire with the circle in the middle your mind just doesn't think the corresponding lumped model of the two resistors of 1/3 in series with the two resistors of 1/6 which are in parallel.
 
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