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title: "A circuit consists of an ideal battery of potential difference \\(\\Delta V\\) connected to three resistors. Resistor 1 has resistance \\(R_1 = R\\), while Resistors 2 and 3 have resistances \\(R_2 = 2R\\) and \\(R_3 = 6R\\), respectively. Resistors 2 and 3 are connected in parallel with each other, and this parallel combination is connected in series with Resistor 1 across the battery. Which of the following correctly ranks the rate of energy dissipation \\(P_1\\), \\(P_2\\), and \\(P_3\\) in Resistors 1, 2, and 3, respectively?"
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url: "https://nerd-notes.com/ubq/118455/"
date_modified: "2026-08-04T08:10:13+00:00"
---

# A circuit consists of an ideal battery of potential difference \(\Delta V\) connected to three resistors. Resistor 1 has resistance \(R_1 = R\), while Resistors 2 and 3 have resistances \(R_2 = 2R\) and \(R_3 = 6R\), respectively. Resistors 2 and 3 are connected in parallel with each other, and this parallel combination is connected in series with Resistor 1 across the battery. Which of the following correctly ranks the rate of energy dissipation \(P_1\), \(P_2\), and \(P_3\) in Resistors 1, 2, and 3, respectively?

A circuit consists of an ideal battery of potential difference \(\Delta V\) connected to three resistors. Resistor 1 has resistance \(R_1 = R\), while Resistors 2 and 3 have resistances \(R_2 = 2R\) and \(R_3 = 6R\), respectively. Resistors 2 and 3 are connected in parallel with each other, and this parallel combination is connected in series with Resistor 1 across the battery. Which of the following correctly ranks the rate of energy dissipation \(P_1\), \(P_2\), and \(P_3\) in Resistors 1, 2, and 3, respectively?

![A schematic diagram of an electric circuit oriented in a rectangular loop. On the vertical left wire, an ideal battery is drawn with potential difference labeled \(\Delta V\), with the longer positive line at the top. The top wire runs horizontally to the right and connects in series to a resistor labeled \(R_1 = R\). Past \(R_1\), the wire reaches a junction node where it splits into two parallel horizontal branches. The top branch contains a resistor labeled \(R_2 = 2R\). The bottom branch contains a resistor labeled \(R_3 = 6R\). To the right of the resistors, the two branches rejoin at a second junction node. A wire then runs down and horizontally left back to the negative terminal at the bottom of the battery. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831013-tDNpYY.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118455/*