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title: "A circuit consists of an ideal battery of potential difference \\(V_0\\) connected to three capacitors with capacitances \\(C\\), \\(2C\\), and \\(3C\\), as shown in the diagram. The capacitors with capacitances \\(C\\) and \\(2C\\) are connected in parallel with each other, and this parallel combination is connected in series with the capacitor of capacitance \\(3C\\). The circuit has reached steady state. In terms of \\(C\\) and \\(V_0\\), what is the total electrostatic potential energy stored in the three-capacitor system?"
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url: "https://nerd-notes.com/ubq/117104/"
date_modified: "2026-08-04T06:17:26+00:00"
---

# A circuit consists of an ideal battery of potential difference \(V_0\) connected to three capacitors with capacitances \(C\), \(2C\), and \(3C\), as shown in the diagram. The capacitors with capacitances \(C\) and \(2C\) are connected in parallel with each other, and this parallel combination is connected in series with the capacitor of capacitance \(3C\). The circuit has reached steady state. In terms of \(C\) and \(V_0\), what is the total electrostatic potential energy stored in the three-capacitor system?

A circuit consists of an ideal battery of potential difference \(V_0\) connected to three capacitors with capacitances \(C\), \(2C\), and \(3C\), as shown in the diagram. The capacitors with capacitances \(C\) and \(2C\) are connected in parallel with each other, and this parallel combination is connected in series with the capacitor of capacitance \(3C\). The circuit has reached steady state. In terms of \(C\) and \(V_0\), what is the total electrostatic potential energy stored in the three-capacitor system?

![A schematic of a DC circuit containing an ideal battery and three capacitors. The battery, labeled V_0, is situated on a left vertical branch with its longer positive plate at the top. A wire extends from the top of the battery horizontally to the right to a top junction. At this junction, the wire splits into two parallel vertical branches: the left branch contains a parallel-plate capacitor labeled C, and the right branch contains a parallel-plate capacitor labeled 2C. The two parallel branches recombine at a lower junction directly below. From this lower junction, a wire extends vertically downward through a third capacitor labeled 3C. From the bottom of the 3C capacitor, the wire turns horizontally left and connects back to the bottom negative terminal of the battery. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785824246-bERrKR.jpg)

- **A.** \(\dfrac{1}{3} C V_0^2\)
- **B.** \(\dfrac{1}{2} C V_0^2\)
- **C.** \(\dfrac{2}{3} C V_0^2\)
- **D.** \(\dfrac{3}{4} C V_0^2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117104/*