Aparallel-plate capacitor is connected to a battery. what happens to the stored energy if the plate separation is doubled while the capacitor remains connected to the battery?

new energy of the capacitor is half that of initial energy

Explanation:

As we know that the energy stored in the capacitor is given as

here we know that capacitance of parallel plate capacitor is given as

V = voltage of battery

so now we have capacitor remains connected to the same battery and the separation between the plates is doubled

so we have

so now the energy stored between the plates is

so new energy of the capacitor is half