A infinite ladder is constructed by connecting several sections of` 2muF,1muF` capacitor combinations as shown in figure . It is terminated by a capacitor of capacitance C . What value should be chosen for C, such that the equivalent capacitance of the number of sections in between ?

Explanation

AB = C and `4 mu F ` are in series So `C_1 and 2 mu F` are imparallel
Then `C_1` and `2 mu F ` are `C = C_1 + 2 mu F`
`rArr 4 C + 8 + 2C = 4C + C^(2)`
`rArr C^(2) - 2C - 8 = 0 `
` C = - 2` (impossible )
So, `C = 4 mu F `
The value of C is `4 mu F`