In the following circuit, the resultant capacitance between `A` and `B` is `1muF`. Then value of `C` is

Options

A. `(32)/(11)muF`
B. `(11)/(32)muF`
C. `(23)/(32)muF`
D. `(32)/(23)muF`

Answer

D

Explanation

`12 muF` and `6 muF` are in series and again are in parallel with `4 muF`.
Therefore, resultant of these three will be
`= (12xx6)/(12 + 6) + 4 = 4+4 = 8 muF`
This equivalent system is in series with `1 muF`.
Its equivalent capacitance `= (8 xx 1)/(8 + 1) = (8)/(9)muF` ..(i)
Equivalent of `8 muF, 2muF` and `2 muF`
`= (4 xx 8)/(4 + 8) = (32)/(12) = (8)/(3) muF` ..(ii)
(i) and (ii) are in parallel and are in series with `C`
`:. (8)/(9) + (8)/(3) = (32)/(9)` and `C_(eq) = 1 = ((32)/(9) xx C)/((32)/(9) + C) rArr C = (32)/(23) muF`