when switch is opened

\(Q\) on \(2^{nd}\) capacitor is \(cv\) even after introduction of dielectric \(Q\) remain same but

\(C\) will become \(KC\)

Energy \(=\frac{ Q ^2}{2 C ^2}=\frac{( cv )^2}{2\left( K _{ l }\right)}=\frac{ cv ^2}{2 k }\)

Energy is set is \(\frac{1}{2} cv ^2\)

same as before

after dielectric insertion

\(c\) become \(kc\)

Energy \(=\frac{1}{2}( kc ) v ^2\)

\(=\frac{ kcv ^2}{2}\)

Total energy initially \(=\frac{1}{2} c v^2+\frac{1}{2} c v^2=c^2 \cdots(1)\)

Total energy after opening switch \(= k \frac{ cv ^2}{2}+\frac{ cv ^2}{2 k }\)

\(=\frac{c v^2}{2}\left( k +\frac{1}{ k }\right)\)

put \(k=3\)

\(=\frac{ cV ^2(10)}{2 \times 3}=\frac{5 CV ^2}{3} \ldots(2)\)

\((1)\) \(\div(2)\)

\(=3 / 5\)