Fig. shows a network of capacitors where the numbers inidicate the capacitance in microfarel. Find the value of capacitance C if the equivalent capacitance between A and B is to be `2 mu F`.

Explanation

In Fig. `2 muF and 2 mu F` capacitors are in parallel. Their equivalent capacitance is `4 mu F` Further `6 muF and 12 muF` capacitors are in seires. Their equivalent capacitance is
`(1)/(C_(s)) = (1)/(6) + (1)/(12) = (3)/(12) = (1)/(4)`, so that `C_(s) = 4 muF`.
These results are shown in fig. In fig `4 muF and 4 muF` capacitors are in parallel. Thier equivalent capacitance is `8 muF`. Further, `8 muF and 4 muF` capacitors are in series with equivalenty capacitance of `8//3 muF`. This is shown in fig.

Again `1 mu F and 8 mu F` capacitors are in series with equivalent capacitance of `(8)/(9) muF`, Fig. Now `(8)/(3) muF and (8)/(9) muF` capacitors are in parallel having equivalent capacitance of `(32)/(9) muF`, Fig. As capacitance C and `(32)/(9) muF` are in series and combined capacitance between A and B is `2 mu F`.
`:. (1)/(2) = (1)/(C ) + (9)/(32)`
`(1)/(C ) = (1)/(2) - (9)/(32) = (16-9)/(32) = (7)/(32)`
`:. C = (32)/(7) muF = 4.57 muF`