Resistance between two junctions in a 2D mesh

In summary, the question asks for the equivalent resistance between any two consecutive junctions in an infinite 2D mesh of conducting wire with a resistance of R between each junction. The solution involves using the principle of superposition of current distribution, where a positive potential is applied at one point and a negative potential at another, resulting in a total current of i/2 flowing through the two points.
  • #1
AdityaDev
527
33

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?
 
Physics news on Phys.org
  • #2
AdityaDev said:

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.
 
  • #3
I got to know that you have to use principle of superposition of current distribution to solve the problem. If I Earth the boundry 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.
 

Attachments

  • 20150426_085627-1.jpg
    20150426_085627-1.jpg
    25.2 KB · Views: 412

What is resistance between two junctions in a 2D mesh?

The resistance between two junctions in a 2D mesh is a measure of how difficult it is for electric current to flow between those two points. It is influenced by the material and dimensions of the mesh as well as the distance between the two junctions.

How is resistance between two junctions in a 2D mesh calculated?

The resistance between two junctions in a 2D mesh can be calculated using Ohm's law, which states that resistance is equal to the voltage difference between the two junctions divided by the current flowing through the mesh. It can also be calculated using the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the mesh, and A is the cross-sectional area of the mesh.

What factors affect the resistance between two junctions in a 2D mesh?

The resistance between two junctions in a 2D mesh is affected by a variety of factors, including the material and dimensions of the mesh, the distance between the two junctions, and the temperature of the mesh. The resistivity of the material also plays a significant role in determining the resistance.

Why is the resistance between two junctions in a 2D mesh important?

The resistance between two junctions in a 2D mesh is important because it affects the flow of electric current through the mesh. A higher resistance means that more energy is lost as heat, which can impact the efficiency of electronic devices and circuits. It is also an important factor to consider in designing and optimizing electronic components.

How can the resistance between two junctions in a 2D mesh be reduced?

The resistance between two junctions in a 2D mesh can be reduced by using materials with lower resistivity, increasing the cross-sectional area of the mesh, or decreasing the distance between the two junctions. Additionally, using thicker and wider conductive paths can also help reduce resistance in a 2D mesh.

Similar threads

Two concentric conducting spherical shells and resistor in between
    • Introductory Physics Homework Help
2
Replies
44
Views
906
Current in a circuit without external resistance
    • Introductory Physics Homework Help
Replies
8
Views
859
Differences in the Brightness of bulbs for 2 separate circuits
    • Introductory Physics Homework Help
Replies
1
Views
1K
Resistance, current and current density
    • Introductory Physics Homework Help
Replies
8
Views
1K
I Resistance and specific resistance relationships
    • Electromagnetism
Replies
16
Views
663
Find the Retarding Force due to Eddy Currents
    • Introductory Physics Homework Help
Replies
5
Views
469
Calculation of equivalent resistance
    • Introductory Physics Homework Help
Replies
5
Views
2K
Why Can't Current Flow Between Two Same Voltage Nodes?
    • Introductory Physics Homework Help
Replies
10
Views
974
Finding the Resistance of a Fault in a Pair of Transmission Lines
    • Introductory Physics Homework Help
Replies
8
Views
1K
Unraveling the Mystery of EMF Internal Resistance
    • Introductory Physics Homework Help
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top