Equivalent resistor of 2011 resistor web

In summary, the conversation discusses finding the equivalent resistor between pairs of points connected by a resistor in a circuit with 2011 points. The solution for 3 and 4 points is provided, but the generalization for 5 or more points is unknown. The conversation also mentions the possibility of using Kirchoff's method, but it is deemed impractical. A diagram is attached for clarification.
  • #1
pincopallino
7
0
1. let's have 2011 point each pair connected by a resitor R. what is the equivalent resistor between each pair of points conneced by R?



2. due to the symmetry the equivalent resistor between two arbitrary point connected by R is always the same. let's take two of this contigouspoins. the voltage at each other point is the same, due to the symmetry (is it right?), but then?



The Attempt at a Solution

 
Physics news on Phys.org
  • #2
pincopallino said:
1. let's have 2011 point each pair connected by a resitor R. what is the equivalent resistor between each pair of points conneced by R?



2. due to the symmetry the equivalent resistor between two arbitrary point connected by R is always the same. let's take two of this contigouspoins. the voltage at each other point is the same, due to the symmetry (is it right?), but then?



The Attempt at a Solution


Can you please describe the problem in more detail, and maybe show us a diagram?

What do you mean by 2011 points? What is their geometry? 2-dimensional, 3-dimensional? What shape?
 
  • #3
in attachment a diagram for 5 points.
 

Attachments

  • Document.pdf
    88.2 KB · Views: 247
  • #4
pincopallino said:
in attachment a diagram for 5 points.

You are required to show your work on schoolwork questions. What is the answer for 3 poinsts? For 5 points? etc.

And where did this question come from?
 
  • #5
it is a question from our teacher.
it is evident that using standard method of resolution (kirchoff or whatever) is absurd, as it would get to a big linear sistem of equations.
for three is easy Req=2/3R. for four, it' s eay as well, as for symmetry reason the free twi point are at hte same voltage, so Req=R/2.
but 5, 6 , 7 ...2011 points? is the generalization that all the other points are equipotential corrct?
 
  • #6
Of course Kirchoff is not an option.
But it looks like you already know the solution, at least partially.
 
  • #7
I would like, but I do not have.
there must be some trick.
isn't there on line in the WEB any free circuit resolutor?
 
  • #8
pincopallino said:
I would like, but I do not have.
there must be some trick.
isn't there on line in the WEB any free circuit resolutor?

Not in this case.
But your intuition was fine.
 

1. What is the purpose of finding the equivalent resistor of a 2011 resistor web?

The purpose of finding the equivalent resistor of a 2011 resistor web is to simplify a complex circuit into a single equivalent resistor that has the same overall resistance as the original circuit. This allows for easier analysis and calculations.

2. How is the equivalent resistor of a 2011 resistor web calculated?

The equivalent resistor of a 2011 resistor web is calculated by using the formula: Req = R1 + R2 + R3 + ... + Rn, where R1, R2, R3, etc. are the individual resistors in the web. This formula is valid for resistors connected in series.

3. Can the equivalent resistor of a 2011 resistor web be calculated for resistors connected in parallel?

Yes, the equivalent resistor of a 2011 resistor web can also be calculated for resistors connected in parallel. The formula for this is: 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn. This formula is valid for resistors connected in parallel.

4. How does the equivalent resistor of a 2011 resistor web affect the overall resistance of a circuit?

The equivalent resistor of a 2011 resistor web represents the overall resistance of the original circuit. This means that if the equivalent resistor is higher, the overall resistance of the circuit will also be higher, and vice versa.

5. Are there any limitations to calculating the equivalent resistor of a 2011 resistor web?

Yes, there are a few limitations to calculating the equivalent resistor of a 2011 resistor web. This method assumes that the resistors are ideal (no internal resistance) and that the temperature remains constant. Additionally, this method is only valid for linear circuits, meaning that the relationship between voltage and current is consistent.

Similar threads

  • Introductory Physics Homework Help
Replies
28
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
835
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
2K
Replies
4
Views
937
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top