A parallel plate capacitor having capacity \( C_0 \) is charged to \( V_0 \). With battery disconnected, if the separation between the plates is doubled, then the energy stored in it is \( E_1 \). Instead if the separation between the plates is doubled, with battery in connection, the energy stored in it is \( E_2 \). Then the value of \( \frac{E_2}{E_1} \) is