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(A) The energy stored in a capacitor is given by $U = Q^2 / (2C)$.Initially,the capacitance is $C = \epsilon_0 A / d$.When the battery is disconnected

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$K$

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(A) The energy stored in a capacitor is given by $U = Q^2 / (2C)$.Initially,the capacitance is $C = \epsilon_0 A / d$.When the battery is disconnected,the charge $Q$ on the plates remains constant.When a dielectric slab of dielectric constant $K$ and thickness $d$ is introduced,the new capacitance becomes $C' = K C$.The new energy stored is $U' = Q^2 / (2C') = Q^2 / (2KC)$.The ratio of the initial energy to the final energy is $U / U' = (Q^2 / 2C) / (Q^2 / 2KC) = K$.

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