Equivalent resistance for an infinite grid

In summary, an infinite grid is a theoretical network of interconnected resistors that is used to represent a complex circuit with an infinite number of resistors. Equivalent resistance for an infinite grid is calculated using the formula R = ρ/2A, and cannot be physically created. It is significant in circuit analysis as it represents the total resistance of the circuit and has a direct impact on the number of resistors in the grid. As the number of resistors increases, the equivalent resistance decreases, approaching 0 as the number of resistors approaches infinity.
  • #1
swapnilster
10
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?
 
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  • #2
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.)
 

1. What is an infinite grid in relation to equivalent resistance?

An infinite grid is a theoretical network of interconnected resistors that extends infinitely in all directions. It is used to represent a complex circuit with an infinite number of resistors, making it easier to calculate the equivalent resistance.

2. How is equivalent resistance calculated for an infinite grid?

Equivalent resistance for an infinite grid is calculated using the formula R = ρ/2A, where ρ is the resistivity of the material and A is the cross-sectional area of the resistors.

3. Can an infinite grid be physically created?

No, an infinite grid is a theoretical concept and cannot be physically created. It is used as a simplification in circuit analysis to make calculations easier.

4. What is the significance of equivalent resistance in an infinite grid?

The equivalent resistance in an infinite grid represents the total resistance of the circuit. It is used to calculate the current and voltage in the circuit, making it an important factor in circuit analysis.

5. How does the number of resistors in an infinite grid affect the equivalent resistance?

The number of resistors in an infinite grid has a direct impact on the equivalent resistance. As the number of resistors increases, the equivalent resistance decreases, approaching a limit of 0 as the number of resistors approaches infinity.

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