Find the capacitance of the infinite ladder between points X and Y, Fig.

Explanation

Let C be the capacitance of the infinite ladder. As the ladder is infinite, addition of one more element of two capacitors `(1 muF and 2 muF)` across the points X and Y should not charge the total capacitance. Therefore, In fig, `2 muF` capacitance is in series with capacitance C.
`:.` Their combined capacity `= (2 xx C)/(2 + C)`
This combination is in parallel with `1 muF` capacitance. The equivalent capacity of the arrangement is
`(1 + (2C)/(2 + C))` which must be equal to C i.e., `(1+n (2C)/(1 + C)) = C`
or `C^(2) + 2C = 2 + 3C` or `C^(2) - C = 0 :. C = 2 or -1`
Capacitance cannot be negative. `:. C = 2 muF`