There is an infinite staircase where each step is a 1 ohm resistor. How do you calculate the equivalent resistance between any of the two points on the staircase?
it depends on how you connect the resistors
if you arrange them in a grid, where they connect both going sideways along the stairs and up/down the stairs, then I think it would tend towards zero
but if you have separate lines of resistors going up/down the stairs then it should be infinite?
I'm imagining this infinte staircase:
+--+ --> | | +--+--+ | | | +--+--+--+ | | | | +--+--+--+--+ --> | | V V
If the staircase has infinite underfill, by symmetry, the resistance of two points on the edge will be twice that between the same two points on the infinite resistor grid plane.