What is the Resistance Between Two Points in an Infinite Grid?

Click For Summary
The discussion centers on calculating the resistance between two points in an infinite grid, where resistance is proportional to length. Initial calculations for specific values of n suggest a decreasing resistance, with values like R=1 for n=1 and R=sqrt(2)/2 for n=2. However, the general solution for infinite resistors remains elusive, with some participants arguing that the equivalent resistance approaches zero as more resistors are added in parallel. Despite this, others assert that the resistance cannot be zero, indicating a contradiction in the understanding of the problem. The conversation highlights the complexities of resistance in infinite networks and the challenges in deriving a general formula.
FermatPell
Messages
21
Reaction score
0

Homework Statement



What is the resistance between A i B if resistance is proportional to length, and the resistance of a side of the largest square is R?

Homework Equations



This is nothing more than a bunch of serial (parallel) resistors.

The Attempt at a Solution



n=1 => R=1
n=2 => R=sqrt(2)/2
n=3 => R=2/3

but i can't find it for general N

w9ejc8.png
 
Physics news on Phys.org
If I understand your problem correctly, the answer is zero resistance, seeing as the more resistors which are added in parallel in a circuit, the lower the resistance. If there are an infinite number, than there is an equivalent resistance of zero.
 
The resistance is definitely greater than zero.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Need help with a question on potential difference
  • · Replies 7 ·
Replies
7
Views
2K
How to find the equivalent resistance of this infinite circuit?
  • · Replies 10 ·
Replies
10
Views
2K
Resistivity equation relating to equations for resistors
  • · Replies 23 ·
Replies
23
Views
2K
Two concentric conducting spherical shells and resistor in between
  • · Replies 44 ·
2
Replies
44
Views
4K
Batteries in series, parallel, and internal resistance
  • · Replies 24 ·
Replies
24
Views
5K
What's the total resistance in this circuit?
  • · Replies 10 ·
Replies
10
Views
2K
Calculate equivalent resistance
  • · Replies 5 ·
Replies
5
Views
2K
Resistance Association - How to solve this exercise in the proper way?
  • · Replies 2 ·
Replies
2
Views
709
Why is resistance of similar cases calculated differently?
  • · Replies 4 ·
Replies
4
Views
2K
Rank in order, from largest to smallest, the resistance (eq)
  • · Replies 2 ·
Replies
2
Views
3K