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(D) The total energy $U$ in an $LC$ circuit is constant and is given by the maximum energy stored in the capacitor: $U = \frac{Q^2}{2C}$.When the char

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$\frac{3U}{4}$

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(D) The total energy $U$ in an $LC$ circuit is constant and is given by the maximum energy stored in the capacitor: $U = \frac{Q^2}{2C}$.When the charge on the capacitor is $Q' = \frac{Q}{2}$,the energy stored in the capacitor $U_C$ is given by:$U_C = \frac{(Q')^2}{2C} = \frac{(Q/2)^2}{2C} = \frac{Q^2/4}{2C} = \frac{Q^2}{8C}$.Since the total energy $U$ is the sum of the energy in the capacitor $U_C$ and the energy in the inductor $U_L$,we have $U = U_C + U_L$.Therefore,the energy stored in the inductor $U_L$ is:$U_L = U - U_C = \frac{Q^2}{2C} - \frac{Q^2}{8C}$.Taking the common denominator:$U_L = \frac{4Q^2 - Q^2}{8C} = \frac{3Q^2}{8C}$.Since $U = \frac{Q^2}{2C}$,we can write $\frac{Q^2}{8C} = \frac{1}{4} U$.Thus,$U_L = \frac{3}{4} U$.

In an oscillating $LC$ circuit,the total stored energy is $U$ and the maximum charge on the capacitor is $Q$. When the charge on the capacitor is $\frac{Q}{2}$,the energy stored in the inductor is:

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