A finite ladder is constructed by connecting several sections of `3 muF,6 muF` capacitor combination as shown. The value of `C` such that the equivalent capacitance of ladder between the points `A` and `B` becomes independent of the number of section in between

Options

A. `2muF`
B. `4muF`
C. `6muF`
D. `8muF`

Answer

C

Explanation

If ladder consist infinite pairs of `3` and `6`, first find `C_(eq)`.
`C_(eq)=C'=3+(6C')/(6+C)`
`(C'-3)(6+C')=6C'`
`C'^(2)-3C'-18=0`
`(C'-6)(C'+3)=0`
`C'=6muF`
`C=6muF`