Equivalent resistance for an infinite grid

Click For Summary
SUMMARY

The equivalent resistance between two adjacent points on an infinite square grid, where each side of every cell has a resistance of r, is established as r/2. This conclusion is derived from the symmetrical properties of the grid and the application of series and parallel resistance calculations. The hint provided suggests that the solution can be intuitively understood through the grid's structure.

PREREQUISITES
  • Understanding of electrical resistance concepts
  • Familiarity with series and parallel resistor combinations
  • Basic knowledge of infinite geometric series
  • Concept of symmetry in electrical networks
NEXT STEPS
  • Explore the derivation of equivalent resistance in infinite networks
  • Study the application of Kirchhoff's laws in complex circuits
  • Learn about the behavior of resistive grids in different configurations
  • Investigate the implications of symmetry in electrical engineering problems
USEFUL FOR

Electrical engineers, physics students, and anyone interested in advanced circuit analysis and the properties of infinite networks.

swapnilster
Messages
10
Reaction score
0
There is an infinite square grid with each side of every cell making up the grid of resistance r.
What is the equivalent resistance between two adjacent points on the grid?
 
Physics news on Phys.org
swapnilster said:
There is an infinite square grid with each side of every cell making up the grid of resistance r.
What is the equivalent resistance between two adjacent points on the grid?

r/2

(Hint: There's an easy way to see this.)
 

Similar threads

High School Resistance Between Two Small Conducting Spheres
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Resistance and specific resistance relationships
  • · Replies 16 ·
Replies
16
Views
2K
High School Troubleshooting Battery Internal Resistance Measurements
  • · Replies 105 ·
4
Replies
105
Views
13K
Graduate Putting internal resistance in series with a voltage source
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad The answer is 15! What is the problem?
  • · Replies 1 ·
Replies
1
Views
2K
High School Axes on a hyperbolic plane
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Determining Thevenin equivalent resistance
  • · Replies 7 ·
Replies
7
Views
2K
How to find the equivalent resistance of this infinite circuit?
  • · Replies 10 ·
Replies
10
Views
3K
High School Found a circuit where current is zero across an ohmic device (dV>0)
  • · Replies 11 ·
Replies
11
Views
1K
Undergrad Are voltage and current waves in transmission lines an artifice?
  • · Replies 6 ·
Replies
6
Views
2K