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title: "In the circuit shown, an ideal battery of electromotive force \\(\\mathcal{E}\\) is connected in series with resistor \\(R_1\\). Resistor \\(R_1\\) is in series with a parallel network consisting of resistor \\(R_2\\) in series with an open switch \\(S\\) in one branch and resistor \\(R_3\\) in the other branch, where \\(R_1 = R_2 = R_3 = R\\). Let \\(P_0\\) be the power dissipated in resistor \\(R_1\\) before switch \\(S\\) is closed, and let \\(P_1\\), \\(P_2\\), and \\(P_3\\) be the power dissipated in resistors \\(R_1\\), \\(R_2\\), and \\(R_3\\), respectively, after switch \\(S\\) is closed. Which of the following correctly ranks the powers \\(P_0\\), \\(P_1\\), \\(P_2\\), and \\(P_3\\)?"
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url: "https://nerd-notes.com/ubq/121581/"
date_modified: "2026-08-23T05:24:09+00:00"
---

# In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with resistor \(R_1\). Resistor \(R_1\) is in series with a parallel network consisting of resistor \(R_2\) in series with an open switch \(S\) in one branch and resistor \(R_3\) in the other branch, where \(R_1 = R_2 = R_3 = R\). Let \(P_0\) be the power dissipated in resistor \(R_1\) before switch \(S\) is closed, and let \(P_1\), \(P_2\), and \(P_3\) be the power dissipated in resistors \(R_1\), \(R_2\), and \(R_3\), respectively, after switch \(S\) is closed. Which of the following correctly ranks the powers \(P_0\), \(P_1\), \(P_2\), and \(P_3\)?

In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with resistor \(R_1\). Resistor \(R_1\) is in series with a parallel network consisting of resistor \(R_2\) in series with an open switch \(S\) in one branch and resistor \(R_3\) in the other branch, where \(R_1 = R_2 = R_3 = R\). Let \(P_0\) be the power dissipated in resistor \(R_1\) before switch \(S\) is closed, and let \(P_1\), \(P_2\), and \(P_3\) be the power dissipated in resistors \(R_1\), \(R_2\), and \(R_3\), respectively, after switch \(S\) is closed. Which of the following correctly ranks the powers \(P_0\), \(P_1\), \(P_2\), and \(P_3\)?

![A single schematic circuit diagram drawn with clean black lines on a white background. On the left vertical branch is a battery symbol consisting of two parallel horizontal lines, with the longer top line labeled with a small plus sign and the shorter bottom line labeled with a small minus sign, with the label \(\mathcal{E}\) to its left. From the top terminal of the battery, a wire extends upward, turns right 90 degrees, and passes through a zigzag resistor symbol labeled \(R_1\). To the right of \(R_1\), the wire splits at a junction into two parallel horizontal branches. The upper branch contains an open switch symbol labeled \(S\) in series with a zigzag resistor labeled \(R_2\). The lower branch contains a zigzag resistor labeled \(R_3\). The two branches rejoin at a right junction, and a single wire continues right, turns downward 90 degrees, turns left 90 degrees, and connects to the bottom terminal of the battery. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-diagram-1787462649-FZ4wN9.jpg)

- **A.** \(P_0 > P_1 > P_2 = P_3\)
- **B.** \(P_1 = P_0 > P_2 = P_3\)
- **C.** \(P_1 > P_2 = P_3 > P_0\)
- **D.** \(P_1 > P_0 > P_2 = P_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121581/*