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31 August, 18:43

Two identical capacitors are connected parallel. Initially they are charged to a potential V0 and each acquired a charge Q0. The battery is then disconnected, and the gap between the plates of one capacitor is filled with a dielectric. (a) What is the new potential difference V across the capacitors. possible asnwers: V = (Vo) ^2/[kQo+Vo), V=Vo/2k, V=Vo/2, V=kQo/Vo, V=2Vo/[k+1]

(b) If the dielectric constant is 7.8, calculate the ratio of the charge on the capacitor with the dielectric after it is inserted as compared with the initial charge.

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  1. 31 August, 18:57
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    capacitance of each capacitor

    C₀ = Q₀ / V₀

    V₀ = Q₀ / C₀

    New total capacitance = C₀ (1 + K)

    Common potential

    = total charge / total capacitance

    = 2 Q₀ / [ C₀ (1 + K) ]

    2 V₀ / (1 + K)

    b)

    Common potential = 2 x V₀ / (1 + 7.8)

    =.227 V₀

    charge on capacitor with dielectric

    =.227 V₀ x 7.8 C₀

    = 1.77 V₀C₀

    = 1.77 Q₀

    Ratio required = 1.77
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