Resistance of this circuit containing a Circular section

In summary, the conversation discusses the calculation of resistance in a circuit with two parallel paths and the confusion over how the resistance of 1/12 ohm is derived. The participants also mention the difficulty in visualizing the circuit and its corresponding lumped model.
  • #1
Aristarchus_
95
7
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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  • #2
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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  • #3
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)?
 
  • #4
Yes exactly, what total resistance you get if you connect two resistors of 1/6 in parallel?
 
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  • #5
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...
 
  • #6
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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FAQ: Resistance of this circuit containing a Circular section

What is the formula for calculating the resistance of a circuit with a circular section?

The formula for calculating the resistance of a circuit with a circular section is R = (ρ * L) / A, where R is resistance, ρ is the resistivity of the material, L is the length of the circular section, and A is the cross-sectional area of the circular section.

How does the diameter of a circular section affect the resistance of a circuit?

The diameter of a circular section directly affects the cross-sectional area of the circuit, which in turn affects the resistance. A larger diameter will result in a larger cross-sectional area and therefore a lower resistance, while a smaller diameter will result in a smaller cross-sectional area and a higher resistance.

Does the material of the circular section impact the resistance of the circuit?

Yes, the material of the circular section does impact the resistance of the circuit. Different materials have different resistivities, which can affect the overall resistance of the circuit. Materials with higher resistivities will result in higher resistance, while materials with lower resistivities will result in lower resistance.

How does the length of the circular section affect the resistance of the circuit?

The length of the circular section directly affects the resistance of the circuit. The longer the length, the higher the resistance will be. This is because resistance is directly proportional to length, meaning that as the length increases, so does the resistance.

Can the resistance of a circuit with a circular section be reduced?

Yes, the resistance of a circuit with a circular section can be reduced by increasing the diameter of the circular section, using a material with a lower resistivity, or shortening the length of the circular section. Additionally, using conductors with a larger cross-sectional area can also help reduce resistance.

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