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AP Physics C: E&M
10.4 Dielectrics
10.3 Capacitors
IntermediateMCQMathematicalProportional Analysis23k
A grayscale schematic showing two side-by-side configurations labeled Capacitor 1 on the left and Capacitor 2 on the right. On the left, a rectangular circuit loop contains an ideal battery on the vertical left wire labeled \(V_0\) and a parallel-plate capacitor on the vertical right wire. The capacitor consists of two parallel horizontal plate segments with a shaded rectangular dielectric slab filling the entire space between them, labeled \(\kappa\). On the right, two isolated horizontal parallel plates of the same size and spacing are shown with no connecting wires, also completely filled by an identical shaded rectangular dielectric slab labeled \(\kappa\). No other labels, lines, text, or axes appear.
Capacitor 1 connected to a battery and capacitor 2 isolated, each with an inserted dielectric.
Two identical air-filled parallel-plate capacitors, designated 1 and 2, each have capacitance \(C_0\) and are initially charged to a potential difference \(V_0\). Capacitor 1 remains connected to its battery while a dielectric slab of dielectric constant \(\kappa\) (where \(\kappa > 1\)) is fully inserted between its plates. Capacitor 2 is disconnected from its battery, isolating the charge on its plates, before an identical dielectric slab is fully inserted between its plates. What is the ratio of the final electrostatic energy stored in capacitor 1 to the final electrostatic energy stored in capacitor 2, \(U_1/U_2\)?

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