## Another resistor problem

Anything goes, but keep it seemly...

### Another resistor problem

Resistors are connected in an infinite ladder, starting at 0 and going up to infinity. Specifically, if y is any non-negative integer, then there is a 1-ohm resistor between (0,y) and (1,y), another 1-ohm resistor between (0,y) and (0,y+1), and a third between (1,y) and (1,y+1).

What is the total resistance between (0,0) and (1,0)?

Bill Smythe
Smythe Dakota

Posts: 563
Joined: 11 February 2006

If the ladder extends up the y-axis to infinity, then adding another 'step' at the bottom will not change the answer.

If the resistance between (0,0) and (0,1) is R, then adding the additional step gives the R between (0,-1) and (1,-1) as a parallel of 1 between (0, 0) and (0,1) directly, and a series of (1+R+1) between (0,1) and (1,1) via the y=1 'step'.

R = 1 in parallel with R+2

= (R +2) / (R+2+1)

= (R+2) / (R+3)

R²+3R = R + 2

R² +2R -2 = 0

R = (-2 ± sqrt(4 +8)) /2 = Sqrt3 - 1
Bigtone53

Posts: 413
Joined: 19 September 2005