Why is the total energy of the system shown in the figure Q^2/2C

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The total energy of the system is represented as Q^2/2C because, at maximum charge Q, the capacitor stores all the energy while the inductor has none. When the capacitor is fully charged, it prevents current flow, resulting in zero energy in the inductor. The potential energy stored in the capacitor is derived from its charge and capacitance. This relationship illustrates the energy dynamics between the capacitor and inductor in the system. Understanding this concept is crucial for grasping the behavior of circuits involving capacitors and inductors.
thed0ctor
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In the picture to the left they're summing up the potential energies but I don't understand why they equal to (Q^2)/2C. Almost like both of them put together is like a giant capacitor? Not sure how they got this any help would be appreciated. This is coming from the book University Physics 13e by Young and Freedman Chapter 30, pg 1006 and 1008
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Patrick
 
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It says the maximum capacitor charge is Q. When the capacitor has maximum charge, it does not let current flow. With no current, the inductor does not have any energy. So, the only thing that has any energy in that scenario is the capacitor.
 
Thanks so much!
 

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