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AP Physics C: E&M
10.3 Capacitors
IntermediateMCQMathematical13.5k
Circuit network of four capacitors connected to a battery.
Circuit network of four capacitors connected to a battery.
A circuit contains an ideal battery supplying potential difference \(V_0\) connected to four capacitors. Capacitor \(C_1\) of capacitance \(2C\) is connected in series with a parallel combination of capacitor \(C_2\) of capacitance \(C\) and capacitor \(C_3\) of capacitance \(C\). This entire upper combination is in parallel with a fourth capacitor \(C_4\) of capacitance \(C\) directly across the battery terminals.

Which of the following correctly pairs the potential difference \(V_1\) across capacitor \(C_1\) and the ratio \(U_2 / U_{\text{total}}\), where \(U_2\) is the electric energy stored in capacitor \(C_2\) and \(U_{\text{total}}\) is the total energy stored in all four capacitors?

ChoicePotential Difference \(V_1\)Energy Ratio \(U_2 / U_{\text{total}}\)
(A)\(\dfrac{1}{2} V_0\)\(\dfrac{1}{8}\)
(B)\(\dfrac{1}{2} V_0\)\(\dfrac{1}{4}\)
(C)\(\dfrac{2}{3} V_0\)\(\dfrac{1}{8}\)
(D)\(\dfrac{2}{3} V_0\)\(\dfrac{1}{6}\)

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