Consider an infinite 2-dimensional grid of squares. Each side of each square is a 1 ohm resistor.?

Question

What resistance would an ohm-meter measure across one of these resistors? Please give details of your solution!

Answer 1

<speculation>

I would suspect that an ohm-meter would read zero ohms due to the infinite number of other resistors connected, effectively, in parallel with the resistor being measured.

With just two 3-ohm grid squares attached to the resisor being measured, the apparent resistance is reduced to 0.6 ohms. Additional parallel paths would further reduce the effective resistance.

</speculation>

Answer 2

This problem comes up all the time.

The answer is 1/2 ohm

The link below shows one way to solve it

Intuitively the answer can't be zero. Replace the network with a continuous resistive sheet. Measure the resistance between a couple of points 1 cm apart. The resistance is not zero.