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title: "Five identical lightbulbs, each of constant resistance \\(R\\) and labeled 1 through 5, are connected to an ideal battery of emf \\(\\mathcal{E}\\) and an open switch \\(S\\), as shown in the circuit diagram. Bulbs 1 and 2 are connected in series across the battery, and bulbs 3 and 4 are connected in series across the battery in parallel with the first pair. A central branch containing bulb 5 and switch \\(S\\) connects the node between bulbs 1 and 2 to the node between bulbs 3 and 4. Which of the following correctly ranks the electrical power output \\(P\\) dissipated by the individual bulbs after switch \\(S\\) is closed?"
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url: "https://nerd-notes.com/ubq/124938/"
date_modified: "2026-09-28T14:12:03+00:00"
---

# Five identical lightbulbs, each of constant resistance \(R\) and labeled 1 through 5, are connected to an ideal battery of emf \(\mathcal{E}\) and an open switch \(S\), as shown in the circuit diagram. Bulbs 1 and 2 are connected in series across the battery, and bulbs 3 and 4 are connected in series across the battery in parallel with the first pair. A central branch containing bulb 5 and switch \(S\) connects the node between bulbs 1 and 2 to the node between bulbs 3 and 4. Which of the following correctly ranks the electrical power output \(P\) dissipated by the individual bulbs after switch \(S\) is closed?

Five identical lightbulbs, each of constant resistance \(R\) and labeled 1 through 5, are connected to an ideal battery of emf \(\mathcal{E}\) and an open switch \(S\), as shown in the circuit diagram. Bulbs 1 and 2 are connected in series across the battery, and bulbs 3 and 4 are connected in series across the battery in parallel with the first pair. A central branch containing bulb 5 and switch \(S\) connects the node between bulbs 1 and 2 to the node between bulbs 3 and 4. Which of the following correctly ranks the electrical power output \(P\) dissipated by the individual bulbs after switch \(S\) is closed?

![A schematic diagram of a DC circuit drawn in grayscale. On the far left, an ideal battery is oriented vertically, with its longer positive plate on top and shorter negative plate on bottom, labeled \(\mathcal{E}\). Conducting wires extend from the top and bottom of the battery to the right, entering a bridge network. The upper path contains lightbulb 1 on the left and lightbulb 2 on the right, meeting at a central top node. The lower path contains lightbulb 3 on the left and lightbulb 4 on the right, meeting at a central bottom node. Each lightbulb is drawn as a circle enclosing a filament loop, labeled with numbers 1, 2, 3, and 4 respectively. A vertical cross-wire connects the central top node to the central bottom node. This cross-wire contains lightbulb 5, labeled 5, connected in series with an open knife switch labeled S. The right ends of the upper and lower paths join at a common return wire leading back to the bottom plate of the battery. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1790604723-oMP9bN.jpg)

- **A.** \(P_1 = P_3 > P_5 > P_2 = P_4\)
- **B.** \(P_1 = P_2 = P_3 = P_4 = P_5\)
- **C.** \(P_1 = P_2 = P_3 = P_4 > P_5\)
- **D.** \(P_5 > P_1 = P_2 = P_3 = P_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124938/*