Resistance of this circuit containing a Circular section

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SUMMARY

The discussion focuses on calculating the total resistance of a circuit containing a circular section with two parallel paths. Participants clarify that the total resistance from two resistors of 1/6 ohm in parallel results in a combined resistance of 1/12 ohm. Additionally, the circuit configuration includes two resistors of 1/3 ohm in series with the parallel combination, leading to a total resistance of 2/3 ohm. The challenge of visualizing the circuit layout is acknowledged, emphasizing the importance of understanding the lumped model representation.

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  • Understanding of electrical resistance and Ohm's Law
  • Knowledge of series and parallel resistor configurations
  • Familiarity with lumped circuit models
  • Ability to visualize circuit diagrams
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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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