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 connecte

Question

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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Jezebel 2 weeks 2021-08-28T18:44:36+00:00 1 Answers 0 views 0

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    2021-08-28T18:45:50+00:00

    Answer:

    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

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