Due to dielectric insertion, new capacitance

\(C_{2}=C K\)

Initial energy stored in capacitor, \(U_{1}=\frac{q^{2}}{2 C}\) 

Final energy stored in capacitor, \(U_{2}=\frac{q^{2}}{2 K C}\) 

Change in energy stored, \(\Delta U=U_{2}-U_{1}\)

\(\Delta U=\frac{q^{2}}{2 C}\left(\frac{1}{K}-1\right)=\frac{1}{2} C V^{2}\left(\frac{1}{K}-1\right)\)

New potential difference between plates

\(V^{\prime}=\frac{q}{C K}=\frac{V}{K}\)