d
\(C =900\,\mu F\)

\(Q = CV =900 \times 10^{-6} \times 100=9 \times 10^{-2}=90\,MC\)

Now

Common potential will be developed across both capacitors by \(kVL\)

Total charge on left plates of capacitors should be conserved.

\(90\,mc +0=2\,cv _0\)

\(cv _0=45\,mc\)

Heat dissipated \(= U _{ i }- U _{ f }\) [Change in energy stored in the capacitors]

\(=\frac{1}{2} \frac{(90\,mc )^2}{900\,\mu F }-2 \times \frac{1}{2} \frac{(45\,mc )^2}{900\,\mu F }\left[ U =\frac{ Q ^2}{2 c }\right]\)

\(=\frac{1}{2 \times 900 \times 10^{-6}}(8100-4050) \times 10^{-6}\)

\(=2.25\,Joule\)

OR

Heat \(=\frac{1}{2} \frac{ C _1 C _2}{ C _1+ C _2}\left( V _1- V _2\right)^2\)

\(=\frac{1}{2} \frac{ C ^2}{2 C }(100-0)^2\)

\(=\frac{1}{2} \frac{900 \times 10^{-6}}{2} \times 10^4=\frac{9}{4} \text { Joule }=2.25 \text { Joule }\)