Two capacitors are identical, except that one is empty and the other is fi lled with a dielectric (k 5 4.50). The empty capacitor is connected to a 12.0-V battery. What must be the potential diff erence across the plates of the capacitor fi lled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

5.66 V

Explanation:

We know that the electrical energy stored by a capacitor W = 1/2CV² where C = capacitance and V = voltage applied.

Let C₁, C₂ and V₁, V₂  be the capacitances and voltages applied to the empty capacitor and that with dielectric respectively, then for the same electrical energy to be stored in both capacitors,

1/2C₁V₁² = 1/2C₂V₂²

So, V₂ = *(√C₁/C₂)V₁  Since C₂ = kC₁

V₂ = 1/√kV₁ = 1/√4.5 × 12 V = 5.66 V