a
Capacitors \(2\, \mu \mathrm{F}\) and \(2\, \mu \mathrm{F}\) are parallel, their equivalent \(=4\, \mu \mathrm{F}\)

\(6 \,\mu \mathrm{F}\) and \(12\, \mu \mathrm{F}\) are in series, their equivalent \(=4\, \mu \mathrm{F}\)

Now \(4 \,\mu F(2 \text { and } 2\, \mu F)\) and \(8\, \mu F\) in series

\(=\frac{3}{8}\, \mu F\)

And \(4\, \mu \mathrm{F}(12 \& 6\, \mu \mathrm{F})\) and \(4\, \mu \mathrm{F}\) in parallel \(=4+4=8\, \mu \mathrm{F}\)

\(8\, \mu \mathrm{F}\) in series with \(1\, \mu \mathrm{F}=\frac{1}{8}+1 \Rightarrow \frac{8}{9}\, \mu \mathrm{F}\)

Now \(C_{e q}=\frac{8}{9}+\frac{8}{3}=\frac{32}{9}\)

\(C_{eq}\) of circuit \(=\frac{32}{9}\)

With \(C-\frac{1}{C_{e q}}=\frac{1}{C}+\frac{9}{32}=1 \Rightarrow C=\frac{32}{23}\)