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title: "A circuit consists of an ideal battery of potential difference \\(V_0\\), three identical resistors each of resistance \\(R\\), and an open switch \\(S\\), as shown in the diagram. Resistors \\(R_1\\) and \\(R_2\\) are connected in series across the battery, while resistor \\(R_3\\) and switch \\(S\\) form a branch connected in parallel across \\(R_2\\). What is the ratio \\(P_f / P_i\\) of the rate of energy dissipation in resistor \\(R_1\\) after switch \\(S\\) is closed to the rate of energy dissipation in resistor \\(R_1\\) before switch \\(S\\) is closed?"
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url: "https://nerd-notes.com/ubq/117241/"
date_modified: "2026-08-04T06:45:05+00:00"
---

# A circuit consists of an ideal battery of potential difference \(V_0\), three identical resistors each of resistance \(R\), and an open switch \(S\), as shown in the diagram. Resistors \(R_1\) and \(R_2\) are connected in series across the battery, while resistor \(R_3\) and switch \(S\) form a branch connected in parallel across \(R_2\). What is the ratio \(P_f / P_i\) of the rate of energy dissipation in resistor \(R_1\) after switch \(S\) is closed to the rate of energy dissipation in resistor \(R_1\) before switch \(S\) is closed?

A circuit consists of an ideal battery of potential difference \(V_0\), three identical resistors each of resistance \(R\), and an open switch \(S\), as shown in the diagram. Resistors \(R_1\) and \(R_2\) are connected in series across the battery, while resistor \(R_3\) and switch \(S\) form a branch connected in parallel across \(R_2\). What is the ratio \(P_f / P_i\) of the rate of energy dissipation in resistor \(R_1\) after switch \(S\) is closed to the rate of energy dissipation in resistor \(R_1\) before switch \(S\) is closed?

![A rectangular circuit diagram oriented horizontally. On the far left vertical branch, an ideal battery is drawn with long positive terminal line on top labeled \(V_0\) and short negative terminal line on bottom. From the top of the battery, a horizontal wire goes right through resistor \(R_1\) to junction A. From junction A, the path splits into two parallel vertical branches that rejoin at junction B below. The left parallel branch contains resistor \(R_2\). The right parallel branch contains resistor \(R_3\) in series with an open switch labeled \(S\). From junction B, a horizontal wire returns left to the bottom negative terminal of the battery. No other components, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785825904-pQJ6Xj.jpg)

- **A.** \(\dfrac{4}{3}\)
- **B.** \(\dfrac{16}{9}\)
- **C.** \(\dfrac{9}{4}\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117241/*