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title: "The circuit shown contains an ideal battery of electromotive force \\(\\mathcal{E}\\), an open switch \\(S\\), four identical incandescent lightbulbs (\\(B_1\\), \\(B_2\\), \\(B_3\\), and \\(B_4\\)) each of constant resistance \\(R\\), and two capacitors (\\(C_1\\) and \\(C_2\\)). Initially, capacitor \\(C_1\\) is completely uncharged, while capacitor \\(C_2\\) is fully charged to a potential difference \\(\\Delta V = \\mathcal{E}\\) with the polarity indicated. At time \\(t = 0\\), switch \\(S\\) is closed. Immediately after the switch is closed, which of the following correctly ranks the brightness of the four bulbs?"
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url: "https://nerd-notes.com/ubq/124937/"
date_modified: "2026-09-28T14:12:03+00:00"
---

# The circuit shown contains an ideal battery of electromotive force \(\mathcal{E}\), an open switch \(S\), four identical incandescent lightbulbs (\(B_1\), \(B_2\), \(B_3\), and \(B_4\)) each of constant resistance \(R\), and two capacitors (\(C_1\) and \(C_2\)). Initially, capacitor \(C_1\) is completely uncharged, while capacitor \(C_2\) is fully charged to a potential difference \(\Delta V = \mathcal{E}\) with the polarity indicated. At time \(t = 0\), switch \(S\) is closed. Immediately after the switch is closed, which of the following correctly ranks the brightness of the four bulbs?

The circuit shown contains an ideal battery of electromotive force \(\mathcal{E}\), an open switch \(S\), four identical incandescent lightbulbs (\(B_1\), \(B_2\), \(B_3\), and \(B_4\)) each of constant resistance \(R\), and two capacitors (\(C_1\) and \(C_2\)). Initially, capacitor \(C_1\) is completely uncharged, while capacitor \(C_2\) is fully charged to a potential difference \(\Delta V = \mathcal{E}\) with the polarity indicated. At time \(t = 0\), switch \(S\) is closed. Immediately after the switch is closed, which of the following correctly ranks the brightness of the four bulbs?

![A grayscale circuit schematic oriented on a rectangular loop. On the left vertical wire is an ideal battery labeled \(\mathcal{E}\), with a longer horizontal line on top and a shorter thicker line on the bottom. On the top horizontal wire, immediately to the right of the battery, is a switch labeled \(S\), drawn tilted upward in the open position. To the right of the switch, the circuit divides into three parallel vertical branches connected across the top and bottom horizontal rails. The first vertical branch contains a circular bulb symbol labeled \(B_1\) in series above a capacitor symbol labeled \(C_1\). The second vertical branch contains two circular bulb symbols in series, the upper labeled \(B_2\) and the lower labeled \(B_3\). The third vertical branch contains a circular bulb symbol labeled \(B_4\) in series above a capacitor symbol labeled \(C_2\); above the top plate of \(C_2\) is a plus sign, below the bottom plate is a minus sign, and next to it is the label \(\Delta V = \mathcal{E}\). No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604723-ZfUH53.jpg)

- **A.** \(B_1 > B_2 = B_3 > B_4\)
- **B.** \(B_2 = B_3 > B_1 = B_4\)
- **C.** \(B_4 > B_2 = B_3 > B_1\)
- **D.** \(B_1 = B_2 = B_3 > B_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124937/*