In this grid of 1 Ohm resistors

In summary, to calculate the total resistance in a grid of 1 Ohm resistors, the formula is R = (n x R), where n is the number of resistors in the grid. If more resistors are added to the grid, the total resistance will increase. The arrangement of the resistors in the grid can also affect the total resistance, with parallel connections resulting in a decrease and series connections resulting in an increase. The use of 1 Ohm resistors in the grid is for creating a simple circuit with a known and easily calculated total resistance, often used in basic circuit experiments or for demonstration purposes. Replacing one of the 1 Ohm resistors with a resistor of a different value will change the total resistance
  • #1
Pagan Harpoon
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http://stevensholland.com/challenge-problem-revisited-from-xkcd-comic/
 
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  • #3
I get 8/3pi Ohms.
 

Related to In this grid of 1 Ohm resistors

1. How do I calculate the total resistance in this grid of 1 Ohm resistors?

To calculate the total resistance in a grid of 1 Ohm resistors, you can use the formula R = (n x R), where n is the number of resistors in the grid. In this case, since all the resistors have a value of 1 Ohm, the total resistance would be equal to the number of resistors in the grid.

2. What happens to the total resistance if I add more resistors to the grid?

If you add more resistors to the grid, the total resistance will increase. This is because resistors in a circuit are connected in series, which means that the total resistance is equal to the sum of all the individual resistors.

3. Can I change the arrangement of the resistors in this grid to affect the total resistance?

Yes, you can change the arrangement of the resistors in the grid to affect the total resistance. If you connect the resistors in parallel instead of in series, the total resistance will decrease. This is because in parallel circuits, the total resistance is equal to the reciprocal of the sum of the reciprocals of each individual resistor.

4. What is the purpose of using 1 Ohm resistors in this grid?

The purpose of using 1 Ohm resistors in this grid is to create a simple circuit with a known and easily calculated total resistance. This is often used in basic circuit experiments or for demonstration purposes in the study of electricity and electronics.

5. Can I replace one of the 1 Ohm resistors with a resistor of a different value?

Yes, you can replace one of the 1 Ohm resistors with a resistor of a different value. This will change the total resistance of the circuit, depending on the value of the new resistor and its placement in the grid. However, it is important to note that a circuit's total resistance is affected by the arrangement and values of all the resistors in the circuit.

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