Question

Two capacitors are identical, except
that one is filled with a dielectric ( = 4.50). The empty capacitor is connected to a 12.0 Volt
battery. What must be the potential difference across the plates of the capacitor filled with a
dielectric so that it stores the same amount of electrical energy as the empty capacitor.

Answer 1

The capacitor with the dielectric will have 4.5 times the C of an empty capacitor with same area and gap size.

Since E = (1/2)CV^2, the dielectric-filled capacitor will require only 1/4.5 = 22.2% of the value of V^2 of the empty one, to have the same stored energy.
(Vfilled)^2 = 12^2/4.5 = 32 Volt^2
Vfilled = 5.66 Volts

Answer 2

The method in the previous comment is correct ^^^