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title: "Four identical resistors, each with resistance \\(R\\), are connected to an ideal battery of electromotive force \\(\\mathcal{E}\\), as shown in the circuit diagram. Resistor \\(R_1\\) is connected in series with a parallel combination consisting of resistor \\(R_2\\) in one branch and resistors \\(R_3\\) and \\(R_4\\) in series in the other branch. Which of the following correctly pairs the total electric power \\(P_{\\text{total}}\\rangle\\) dissipated by the circuit with the ranking of the individual powers \\(P_1, P_2, P_3,\\) and \\(P_4\\) dissipated by each resistor?"
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url: "https://nerd-notes.com/ubq/118342/"
date_modified: "2026-08-04T08:09:37+00:00"
---

# Four identical resistors, each with resistance \(R\), are connected to an ideal battery of electromotive force \(\mathcal{E}\), as shown in the circuit diagram. Resistor \(R_1\) is connected in series with a parallel combination consisting of resistor \(R_2\) in one branch and resistors \(R_3\) and \(R_4\) in series in the other branch. Which of the following correctly pairs the total electric power \(P_{\text{total}}\rangle\) dissipated by the circuit with the ranking of the individual powers \(P_1, P_2, P_3,\) and \(P_4\) dissipated by each resistor?

Four identical resistors, each with resistance \(R\), are connected to an ideal battery of electromotive force \(\mathcal{E}\), as shown in the circuit diagram. Resistor \(R_1\) is connected in series with a parallel combination consisting of resistor \(R_2\) in one branch and resistors \(R_3\) and \(R_4\) in series in the other branch. Which of the following correctly pairs the total electric power \(P_{\text{total}}\rangle\) dissipated by the circuit with the ranking of the individual powers \(P_1, P_2, P_3,\) and \(P_4\) dissipated by each resistor?

![A circuit schematic showing an ideal battery on the left labeled \mathcal{E}, with its longer positive terminal on top and shorter negative terminal on bottom. A wire extends from the top terminal to resistor R_1 positioned horizontally. After R_1, the wire meets a junction splitting into two vertical parallel branches. The left parallel branch contains resistor R_2 oriented vertically. The right parallel branch contains two resistors in series, labeled R_3 and R_4, oriented vertically one above the other. Below the parallel branches, the wires rejoin at a bottom junction and connect back to the negative terminal of the battery. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830977-QMDTak.jpg)

- **A.** Total Power: \(\dfrac{5\mathcal{E}^2}{3R}\) | Power Ranking: \(P_1 > P_2 = P_3 = P_4\)
- **B.** Total Power: \(\dfrac{3\mathcal{E}^2}{5R}\) | Power Ranking: \(P_1 > P_3 = P_4 > P_2\)
- **C.** Total Power: \(\dfrac{5\mathcal{E}^2}{3R}\) | Power Ranking: \(P_1 > P_2 > P_3 = P_4\)
- **D.** Total Power: \(\dfrac{3\mathcal{E}^2}{5R}\) | Power Ranking: \(P_1 > P_2 > P_3 = P_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118342/*