Resistance between two junctions in a 2D mesh

[AdityaDev]

Homework Statement

There is an infinite 2D mesh of conducting wire. Resistance between any two consecutive junctions is R. What is the equivalent resistance between any two consecutive junctions?

Homework Equations

The Attempt at a Solution

Every junction is connected to four points and one of it is connected to the required point. For example, if I start from 0,0 then I have to find the resistance between 0,0 and 1,1. Two wires can go to 1,1 by first moving up and then right or moving right and then up, each step having resistance R. But there are infinite ways to reach 1,1. So wouldn't the resistance be infinite?

 

[SammyS]

Homework Statement

There is an infinite 2D mesh of conducting wire. Resistance between any two consecutive junctions is R. What is the equivalent resistance between any two consecutive junctions?

Homework Equations

The Attempt at a Solution

Every junction is connected to four points and one of it is connected to the required point. For example, if I start from 0,0 then I have to find the resistance between 0,0 and 1,1. Two wires can go to 1,1 by first moving up and then right or moving right and then up, each step having resistance R. But there are infinite ways to reach 1,1. So wouldn't the resistance be infinite?

The more paths that are available, the lower the equivalent resistance.

The description you give is not clear (to me).

Can you show some image? Also post the complete question as it was given to you.

 

[AdityaDev]

I got to know that you have to use principle of superposition of current distribution to solve the problem. If I Earth the boundary of mesh(at infinity) and apply a positive potential E at A, then I/4 current flows from A to all four neighbouring points and keeps dividing as it moves from A to infinity. So i/4 flows from A to B and potential at B is V.
If I connect a negitive E at B, currenys from infinity flows towards B and finally i/4 flows from A to B. Let potrntial at A be V.
So total current through AB is i/2.