---
title: "In the circuit shown, an ideal battery of potential difference \\(\\mathcal{E}\\) is connected in series with a resistor \\(R_1\\) of resistance \\(R\\). This combination is connected to two parallel branches: one branch contains resistor \\(R_2\\) of resistance \\(R\\), and the other branch contains resistor \\(R_3\\) of resistance \\(R\\) in series with a capacitor of capacitance \\(C\\) that has a switch \\(S\\) connected in parallel across it. Initially, the switch is closed and the circuit reaches steady state, after which the switch is opened and the circuit reaches a new steady state. What is the ratio of the power dissipated in resistor \\(R_2\\) in the new steady state to that in the initial steady state, \\(\\dfrac{P_{\\text{new}}}{P_{\\text{initial}}}\\)?"
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/124820/"
date_modified: "2026-09-28T14:11:31+00:00"
---

# In the circuit shown, an ideal battery of potential difference \(\mathcal{E}\) is connected in series with a resistor \(R_1\) of resistance \(R\). This combination is connected to two parallel branches: one branch contains resistor \(R_2\) of resistance \(R\), and the other branch contains resistor \(R_3\) of resistance \(R\) in series with a capacitor of capacitance \(C\) that has a switch \(S\) connected in parallel across it. Initially, the switch is closed and the circuit reaches steady state, after which the switch is opened and the circuit reaches a new steady state. What is the ratio of the power dissipated in resistor \(R_2\) in the new steady state to that in the initial steady state, \(\dfrac{P_{\text{new}}}{P_{\text{initial}}}\)?

In the circuit shown, an ideal battery of potential difference \(\mathcal{E}\) is connected in series with a resistor \(R_1\) of resistance \(R\). This combination is connected to two parallel branches: one branch contains resistor \(R_2\) of resistance \(R\), and the other branch contains resistor \(R_3\) of resistance \(R\) in series with a capacitor of capacitance \(C\) that has a switch \(S\) connected in parallel across it. Initially, the switch is closed and the circuit reaches steady state, after which the switch is opened and the circuit reaches a new steady state. What is the ratio of the power dissipated in resistor \(R_2\) in the new steady state to that in the initial steady state, \(\dfrac{P_{\text{new}}}{P_{\text{initial}}}\)?

![A rectangular circuit schematic drawn in thin black lines on a white background. On the left vertical wire is an ideal battery symbol with long upper plate labeled positive and short lower plate labeled negative, accompanied by the label \(\mathcal{E}\) to its left. The top horizontal wire runs from the battery through a resistor zigzag symbol labeled \(R_1\), then reaches a junction that splits into two vertical parallel branches. The middle vertical branch contains a resistor zigzag symbol labeled \(R_2\). The right vertical branch contains a resistor zigzag symbol labeled \(R_3\) above a parallel-plate capacitor symbol labeled \(C\). Connected in parallel across the capacitor symbol is a bypass loop containing an open single-pole single-throw switch labeled \(S\). The bottom horizontal wire connects the bottoms of the middle branch, right branch, and battery to form a complete closed circuit. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604691-iHDiiC.jpg)

- **A.** \(\dfrac{3}{2}\)
- **B.** \(\dfrac{9}{4}\)
- **C.** \(3\)
- **D.** \(9\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124820/*