---
title: "A circuit consists of an ideal battery of emf \\(\\varepsilon\\), an open switch \\(S\\), three resistors with resistances \\(R\\), \\(2R\\), and \\(R\\), and an initially uncharged capacitor of capacitance \\(C\\), connected as shown in the diagram. At time \\(t = 0\\), switch \\(S\\) is closed. In terms of \\(\\varepsilon\\) and \\(R\\), what are the currents through the battery immediately after switch \\(S\\) is closed and a long time after switch \\(S\\) is closed?"
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/120427/"
date_modified: "2026-08-23T04:34:35+00:00"
---

# A circuit consists of an ideal battery of emf \(\varepsilon\), an open switch \(S\), three resistors with resistances \(R\), \(2R\), and \(R\), and an initially uncharged capacitor of capacitance \(C\), connected as shown in the diagram. At time \(t = 0\), switch \(S\) is closed. In terms of \(\varepsilon\) and \(R\), what are the currents through the battery immediately after switch \(S\) is closed and a long time after switch \(S\) is closed?

A circuit consists of an ideal battery of emf \(\varepsilon\), an open switch \(S\), three resistors with resistances \(R\), \(2R\), and \(R\), and an initially uncharged capacitor of capacitance \(C\), connected as shown in the diagram. At time \(t = 0\), switch \(S\) is closed. In terms of \(\varepsilon\) and \(R\), what are the currents through the battery immediately after switch \(S\) is closed and a long time after switch \(S\) is closed?

![A rectangular schematic diagram of a DC circuit. On the left vertical segment is an ideal battery labeled \(\varepsilon\), with the longer positive plate at the top. The top wire extends to the right, containing an open switch labeled \(S\) and a resistor labeled \(R\). To the right of resistor \(R\), the wire reaches a junction that splits into two parallel vertical branches. The middle vertical branch contains a single resistor labeled \(2R\). The right vertical branch contains an uncharged capacitor labeled \(C\) in series above a resistor labeled \(R\). The bottom ends of both vertical branches connect to a common bottom horizontal wire that returns to the negative terminal of the battery. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/circuit-diagram-1-1787459675-PomzAO.jpg)

- **A.** Immediately after: \(\dfrac{\varepsilon}{R}\) Long after: \(\dfrac{\varepsilon}{2R}\)
- **B.** Immediately after: \(\dfrac{\varepsilon}{3R}\) Long after: \(\dfrac{3\varepsilon}{5R}\)
- **C.** Immediately after: \(\dfrac{3\varepsilon}{5R}\) Long after: \(\dfrac{\varepsilon}{3R}\)
- **D.** Immediately after: \(\dfrac{3\varepsilon}{5R}\) Long after: \(\dfrac{\varepsilon}{2R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120427/*