---
title: "The circuit shown consists of an ideal battery of electromotive force \\(\\varepsilon\\), three resistors of resistances \\(R_1\\), \\(R_2\\), and \\(R_3\\), an initially uncharged capacitor of capacitance \\(C\\), and a switch \\(S\\). At time \\(t = 0\\), switch \\(S\\) is closed. After the circuit reaches a steady state, which of the following expressions is equal to the total electric energy stored in the capacitor?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/120420/"
date_modified: "2026-08-23T04:34:33+00:00"
---

# The circuit shown consists of an ideal battery of electromotive force \(\varepsilon\), three resistors of resistances \(R_1\), \(R_2\), and \(R_3\), an initially uncharged capacitor of capacitance \(C\), and a switch \(S\). At time \(t = 0\), switch \(S\) is closed. After the circuit reaches a steady state, which of the following expressions is equal to the total electric energy stored in the capacitor?

The circuit shown consists of an ideal battery of electromotive force \(\varepsilon\), three resistors of resistances \(R_1\), \(R_2\), and \(R_3\), an initially uncharged capacitor of capacitance \(C\), and a switch \(S\). At time \(t = 0\), switch \(S\) is closed. After the circuit reaches a steady state, which of the following expressions is equal to the total electric energy stored in the capacitor?

![A schematic diagram of a DC circuit. On the far left, a vertical branch contains an ideal battery of electromotive force \(\varepsilon\), with the longer positive plate on top and the shorter negative plate on the bottom. From the top of the battery, a horizontal wire extends rightward to a series resistor labeled \(R_1\), followed by a switch labeled \(S\). To the right of the switch, the circuit splits at an upper junction into two parallel vertical branches. The left parallel branch contains a single resistor labeled \(R_3\). The right parallel branch contains a resistor labeled \(R_2\) in series with and positioned above a capacitor labeled \(C\), represented by two equal-length parallel horizontal plates. The bottom ends of both parallel branches rejoin at a lower junction and connect back to the bottom terminal of the battery via a horizontal wire. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459673-5XRb9P.jpg)

- **A.** \(\dfrac{C \varepsilon^2 R_2^2}{2(R_1 + R_2)^2}\)
- **B.** \(\dfrac{C \varepsilon^2 R_3^2}{2(R_1 + R_2 + R_3)^2}\)
- **C.** \(\dfrac{C \varepsilon^2 (R_2 R_3)^2}{2[R_1(R_2 + R_3) + R_2 R_3]^2}\)
- **D.** \(\dfrac{C \varepsilon^2 R_3^2}{2(R_1 + R_3)^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120420/*