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?

Question

Marlee Yang

Physics

15 August, 02:54

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?

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Answers (1)

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Karla Gaines · Answer 1

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