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

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SUMMARY

The total energy of the system is represented as Q^2/2C, where Q is the maximum charge on the capacitor and C is its capacitance. In this scenario, when the capacitor reaches its maximum charge, it prevents current flow, resulting in the inductor holding no energy. Therefore, the energy in the system is solely attributed to the capacitor, confirming the relationship derived in University Physics 13e by Young and Freedman.

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  • Study the derivation of energy stored in capacitors using the formula U = Q^2/2C
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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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