---
title: "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?  | Choice | Potential 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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url: "https://nerd-notes.com/ubq/118214/"
date_modified: "2026-08-04T08:08:12+00:00"
---

# 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?

| Choice | Potential 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) | \(\dfrac{2}{3} V_0\) | \(\dfrac{1}{6}\) |

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?

| Choice | Potential 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) | \(\dfrac{2}{3} V_0\) | \(\dfrac{1}{6}\) |

![A schematic circuit diagram drawn in black lines on a white background. On the far left is a DC battery with two horizontal terminal lines; the long line is marked with a plus sign, labeled V_0. The top wire from the battery extends to the right and splits at a node into two parallel branches. The lower parallel branch contains a single capacitor labeled C_4. The upper parallel branch contains a capacitor labeled C_1 in series with a sub-network consisting of two parallel capacitors labeled C_2 and C_3. The two parallel branches recombine on the right side and connect back to the negative terminal of the battery on the bottom wire. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830892-RL1iou.jpg)

- **A.** \(V_1 = \dfrac{1}{2} V_0\) and \(\dfrac{U_2}{U_{\text{total}}} = \dfrac{1}{8}\)
- **B.** \(V_1 = \dfrac{1}{2} V_0\) and \(\dfrac{U_2}{U_{\text{total}}} = \dfrac{1}{4}\)
- **C.** \(V_1 = \dfrac{2}{3} V_0\) and \(\dfrac{U_2}{U_{\text{total}}} = \dfrac{1}{8}\)
- **D.** \(V_1 = \dfrac{2}{3} V_0\) and \(\dfrac{U_2}{U_{\text{total}}} = \dfrac{1}{6}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118214/*