A finit 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 ladder between the points A and B becomes independent of the number of sections in between ?

Explanation

The equivalent capacitance of the ladder between `A` and `B` becomes independent of the number of sections in between If we remove all the capacitors other than `C`, the equivalent capacitance should also be `C`, In the last until, `C` and `4 muF` are in series, so `C_(1)` and `2 muF` are in parallel Then
`C=C_(1)+2 muF`
or `4C+8+2C+C^(2)` or `C^(2)-2C-8=0`
or `(C+2)(C-4)=0`
Since `C=-2` is impossible, so `C = 4 muF`.