Resistance of this circuit containing a Circular section

AI Thread Summary
The discussion focuses on calculating the resistance of a circuit with a circular section and straight paths. Participants clarify that there are two parallel paths from points C to D, each with a resistance of 1/6 ohm. When these two resistors are connected in parallel, the total resistance is calculated to be 1/12 ohm. The conversation highlights the difficulty in visualizing the circuit layout and understanding the lumped model representation. Ultimately, the participants agree on the resistance values and their implications for the circuit analysis.
Aristarchus_
Messages
95
Reaction score
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?
 
Physics news on Phys.org
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?
 
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?
 
  • Like
Likes Aristarchus_ and hutchphd
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.
 
  • Like
Likes Aristarchus_
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'
Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is(Figure 2): F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
Back
Top