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title: "Three lightbulbs with individual resistances \\(R\\), \\(2R\\), and \\(3R\\) are connected in series to an ideal power supply that maintains a constant potential difference \\(V_0\\). The total rate of energy dissipation in this series circuit is \\(P_{\\text{series}}\\). The three lightbulbs are then disconnected and reconnected in parallel across the same power supply, where the total rate of energy dissipation is \\(P_{\\text{parallel}}\\). What is the ratio \\(\\dfrac{P_{\\text{parallel}}}{P_{\\text{series}}}\\)?"
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url: "https://nerd-notes.com/ubq/118463/"
date_modified: "2026-08-04T08:10:20+00:00"
---

# Three lightbulbs with individual resistances \(R\), \(2R\), and \(3R\) are connected in series to an ideal power supply that maintains a constant potential difference \(V_0\). The total rate of energy dissipation in this series circuit is \(P_{\text{series}}\). The three lightbulbs are then disconnected and reconnected in parallel across the same power supply, where the total rate of energy dissipation is \(P_{\text{parallel}}\). What is the ratio \(\dfrac{P_{\text{parallel}}}{P_{\text{series}}}\)?

Three lightbulbs with individual resistances \(R\), \(2R\), and \(3R\) are connected in series to an ideal power supply that maintains a constant potential difference \(V_0\). The total rate of energy dissipation in this series circuit is \(P_{\text{series}}\). The three lightbulbs are then disconnected and reconnected in parallel across the same power supply, where the total rate of energy dissipation is \(P_{\text{parallel}}\). What is the ratio \(\dfrac{P_{\text{parallel}}}{P_{\text{series}}}\)?

![Two circuit schematics arranged side-by-side. On the left, labeled (a), a single rectangular loop contains an ideal DC voltage source on the left vertical wire labeled \(V_0\) with a long top bar (+) and short bottom bar (-), and three resistor zig-zag symbols in series on the top horizontal wire, labeled from left to right as \(R\), \(2R\), and \(3R\). On the right, labeled (b), a rectangular circuit contains an ideal DC voltage source on the left vertical wire labeled \(V_0\) with a long top bar (+) and short bottom bar (-), connected to three parallel vertical branches to its right. Each parallel branch contains a single resistor zig-zag symbol, labeled from left to right as \(R\), \(2R\), and \(3R\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831020-Kyi3Sq.jpg)

- **A.** \(\dfrac{11}{36}\)
- **B.** \(\dfrac{11}{6}\)
- **C.** \(6\)
- **D.** \(11\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118463/*