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Before inserting dielectric capacitance is given \(\mathrm{C}_0=12.5 \mathrm{pF}\) and charge on the capacitor \(\mathrm{Q}=\mathrm{C}_0 \mathrm{~V}\) After inserting dielectric capacitance will become \(\epsilon_{\mathrm{s}} \mathrm{C}_0\).

Change in potential energy of the capacitor

\(=\mathrm{E}_{\mathrm{i}}-\mathrm{E}_{\mathrm{r}}\)

\(=\frac{\mathrm{Q}^2}{2 \mathrm{C}_{\mathrm{i}}}-\frac{\mathrm{Q}^2}{2 \mathrm{C}_{\mathrm{f}}}=\frac{\mathrm{Q}^2}{2 \mathrm{C}_0}\left[1-\frac{1}{\epsilon_{\mathrm{r}}}\right]\)

\(=\frac{\left(\mathrm{C}_0 \mathrm{~V}\right)^2}{2 \mathrm{C}_0}\left[1-\frac{1}{\epsilon_{\mathrm{r}}}\right]=\frac{1}{2} \mathrm{C}_0 \mathrm{~V}^2\left[1-\frac{1}{\epsilon_{\mathrm{r}}}\right]\)

Using \(\mathrm{C}_0=12.5 \mathrm{pF}, \mathrm{V}=12 \mathrm{~V}, \epsilon_{\mathrm{r}}=6\)

\(=\frac{1}{2}(12.5) \times 12^2\left[1-\frac{1}{6}\right]=\frac{1}{2}(12.5) \times 12^2 \times\)

\(\frac{5}{6}\)

\(=750 \mathrm{pJ}=750 \times 10^{-12} \mathrm{~J}\)