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title: "Five identical capacitors, each of capacitance \\(C\\), are connected in a bridge network across an ideal power supply maintaining a constant potential difference \\(V_0\\). Capacitors \\(C_1\\) and \\(C_2\\) are in series in the top branch, while \\(C_3\\) and \\(C_4\\) are in series in the bottom branch. Capacitor \\(C_5\\) forms a central bridge wire connecting the node between \\(C_1\\) and \\(C_2\\) to the node between \\(C_3\\) and \\(C_4\\). Consider three operational states of the network:  State I: All five capacitors function normally. State II: Central capacitor \\(C_5\\) breaks down under voltage stress and becomes short-circuited. State III: Outer capacitor \\(C_1\\) breaks down under voltage stress and becomes short-circuited.  Which of the following correctly ranks the total electrostatic energy \\(U\\) stored in the network for these three states?"
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url: "https://nerd-notes.com/ubq/118298/"
date_modified: "2026-08-04T08:08:47+00:00"
---

# Five identical capacitors, each of capacitance \(C\), are connected in a bridge network across an ideal power supply maintaining a constant potential difference \(V_0\). Capacitors \(C_1\) and \(C_2\) are in series in the top branch, while \(C_3\) and \(C_4\) are in series in the bottom branch. Capacitor \(C_5\) forms a central bridge wire connecting the node between \(C_1\) and \(C_2\) to the node between \(C_3\) and \(C_4\). Consider three operational states of the network:

State I: All five capacitors function normally.
State II: Central capacitor \(C_5\) breaks down under voltage stress and becomes short-circuited.
State III: Outer capacitor \(C_1\) breaks down under voltage stress and becomes short-circuited.

Which of the following correctly ranks the total electrostatic energy \(U\) stored in the network for these three states?

Five identical capacitors, each of capacitance \(C\), are connected in a bridge network across an ideal power supply maintaining a constant potential difference \(V_0\). Capacitors \(C_1\) and \(C_2\) are in series in the top branch, while \(C_3\) and \(C_4\) are in series in the bottom branch. Capacitor \(C_5\) forms a central bridge wire connecting the node between \(C_1\) and \(C_2\) to the node between \(C_3\) and \(C_4\). Consider three operational states of the network:

State I: All five capacitors function normally.
State II: Central capacitor \(C_5\) breaks down under voltage stress and becomes short-circuited.
State III: Outer capacitor \(C_1\) breaks down under voltage stress and becomes short-circuited.

Which of the following correctly ranks the total electrostatic energy \(U\) stored in the network for these three states?

![A circuit schematic showing a bridge network of five identical capacitors connected across terminals A and B, which maintain a constant potential difference V_0. Terminal A is on the left and terminal B is on the right. Current enters at terminal A and splits into two parallel branches. The upper branch contains capacitor C_1 followed by node X, then capacitor C_2 leading to terminal B. The lower branch contains capacitor C_3 followed by node Y, then capacitor C_4 leading to terminal B. A central vertical wire containing capacitor C_5 connects node X and node Y. Each of the five capacitors is represented by standard parallel-plate capacitor symbols and labeled C_1, C_2, C_3, C_4, and C_5 respectively. No other components or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830927-mMmSWa.jpg)

- **A.** \(U_{III} < U_{II} < U_I\)
- **B.** \(U_{III} < U_I = U_{II}\)
- **C.** \(U_I < U_{II} < U_{III}\)
- **D.** \(U_I = U_{II} < U_{III}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118298/*