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title: "The circuit shown consists of three interconnected loops formed by four vertical branches connected across horizontal top and bottom conducting rails of negligible resistance. Branch 1 contains an ideal battery of emf \\(\\mathcal{E}_1 = 4\\mathcal{E}_0\\) in series with a resistor of resistance \\(R_1 = R\\); branch 2 contains a resistor of resistance \\(R_2 = R\\); branch 3 contains an ideal battery of emf \\(\\mathcal{E}_2 = 2\\mathcal{E}_0\\) in series with a resistor of resistance \\(R_3 = R\\); and branch 4 contains an open switch \\(S\\) in series with an ideal battery of emf \\(\\mathcal{E}_3 = 6\\mathcal{E}_0\\) and a resistor of resistance \\(R_4 = R\\). All battery positive terminals are directed toward the top rail. Which row correctly indicates how the magnitude of the current through resistor \\(R_1\\), the magnitude of the current through resistor \\(R_2\\), and the rate of energy dissipation in resistor \\(R_3\\) change when switch \\(S\\) is closed?"
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url: "https://nerd-notes.com/ubq/124951/"
date_modified: "2026-09-28T14:12:04+00:00"
---

# The circuit shown consists of three interconnected loops formed by four vertical branches connected across horizontal top and bottom conducting rails of negligible resistance. Branch 1 contains an ideal battery of emf \(\mathcal{E}_1 = 4\mathcal{E}_0\) in series with a resistor of resistance \(R_1 = R\); branch 2 contains a resistor of resistance \(R_2 = R\); branch 3 contains an ideal battery of emf \(\mathcal{E}_2 = 2\mathcal{E}_0\) in series with a resistor of resistance \(R_3 = R\); and branch 4 contains an open switch \(S\) in series with an ideal battery of emf \(\mathcal{E}_3 = 6\mathcal{E}_0\) and a resistor of resistance \(R_4 = R\). All battery positive terminals are directed toward the top rail. Which row correctly indicates how the magnitude of the current through resistor \(R_1\), the magnitude of the current through resistor \(R_2\), and the rate of energy dissipation in resistor \(R_3\) change when switch \(S\) is closed?

The circuit shown consists of three interconnected loops formed by four vertical branches connected across horizontal top and bottom conducting rails of negligible resistance. Branch 1 contains an ideal battery of emf \(\mathcal{E}_1 = 4\mathcal{E}_0\) in series with a resistor of resistance \(R_1 = R\); branch 2 contains a resistor of resistance \(R_2 = R\); branch 3 contains an ideal battery of emf \(\mathcal{E}_2 = 2\mathcal{E}_0\) in series with a resistor of resistance \(R_3 = R\); and branch 4 contains an open switch \(S\) in series with an ideal battery of emf \(\mathcal{E}_3 = 6\mathcal{E}_0\) and a resistor of resistance \(R_4 = R\). All battery positive terminals are directed toward the top rail. Which row correctly indicates how the magnitude of the current through resistor \(R_1\), the magnitude of the current through resistor \(R_2\), and the rate of energy dissipation in resistor \(R_3\) change when switch \(S\) is closed?

![A circuit schematic with four parallel vertical branches connected between a continuous top horizontal rail and a continuous bottom horizontal rail. From left to right: Branch 1 contains a DC voltage source labeled \(\mathcal{E}_1 = 4\mathcal{E}_0\) with the longer positive plate on top, in series with a zigzag resistor symbol labeled \(R_1 = R\). Branch 2 contains a single zigzag resistor symbol labeled \(R_2 = R\). Branch 3 contains a DC voltage source labeled \(\mathcal{E}_2 = 2\mathcal{E}_0\) with the longer positive plate on top, in series with a zigzag resistor symbol labeled \(R_3 = R\). Branch 4 contains an open single-pole single-throw switch labeled \(S\), in series with a DC voltage source labeled \(\mathcal{E}_3 = 6\mathcal{E}_0\) with the longer positive plate on top, and a zigzag resistor symbol labeled \(R_4 = R\). Solid black lines represent ideal connecting wires. No other labels, meters, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1790604724-9KCvdj.jpg)

- **A.** | Current in \(R_1\): Increases | Current in \(R_2\): Decreases | Power in \(R_3\): Decreases |
- **B.** | Current in \(R_1\): Decreases | Current in \(R_2\): Increases | Power in \(R_3\): Increases |
- **C.** | Current in \(R_1\): Decreases | Current in \(R_2\): Decreases | Power in \(R_3\): Increases |
- **D.** | Current in \(R_1\): Increases | Current in \(R_2\): Increases | Power in \(R_3\): Decreases |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124951/*