The figure shows a network of capacitance consisting of several repetitive units shown by doted square and a capacitor capacitance `C_(1)` connected as end as shown in the figure.
Find the value of `C_(1)` such that the equivalent capacitance between `A` and `B` is independent of the number of units.

Explanation

The equivalent capacitance between `A` and `B` will be independent of number of units if addition of one or more units to `C_(1)` does not change its value.
The situation is shown in figure. The equivalent between `A'` and `B'` is still `C_(1)`.
`(C_(1)xx2C)/(C_(1)+2C)+C=C_(1)`
`rArr C_(1)=(C+-3C)/(2)`
`:. C_(1)=2C`.