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title: "In the circuit shown, an ideal battery of electromotive force \\(\\mathcal{E}\\) is connected in series with an open switch \\(S\\). The switch is in series with two parallel branches. Branch 1 contains a resistor of resistance \\(R\\) connected in series with an initially uncharged capacitor of capacitance \\(C\\), carrying branch current \\(I_1\\), while Branch 2 contains a resistor of resistance \\(R\\) connected in series with a parallel combination of a second resistor of resistance \\(R\\) and a second initially uncharged capacitor of capacitance \\(C\\), carrying total branch current \\(I_2\\). Which of the following correctly indicates the current \\(I_1\\) immediately after switch \\(S\\) is closed, the current \\(I_2\\) immediately after switch \\(S\\) is closed, and the current \\(I_2\\) a long time after switch \\(S\\) is closed?"
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url: "https://nerd-notes.com/ubq/124972/"
date_modified: "2026-09-28T14:12:23+00:00"
---

# In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with an open switch \(S\). The switch is in series with two parallel branches. Branch 1 contains a resistor of resistance \(R\) connected in series with an initially uncharged capacitor of capacitance \(C\), carrying branch current \(I_1\), while Branch 2 contains a resistor of resistance \(R\) connected in series with a parallel combination of a second resistor of resistance \(R\) and a second initially uncharged capacitor of capacitance \(C\), carrying total branch current \(I_2\). Which of the following correctly indicates the current \(I_1\) immediately after switch \(S\) is closed, the current \(I_2\) immediately after switch \(S\) is closed, and the current \(I_2\) a long time after switch \(S\) is closed?

In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with an open switch \(S\). The switch is in series with two parallel branches. Branch 1 contains a resistor of resistance \(R\) connected in series with an initially uncharged capacitor of capacitance \(C\), carrying branch current \(I_1\), while Branch 2 contains a resistor of resistance \(R\) connected in series with a parallel combination of a second resistor of resistance \(R\) and a second initially uncharged capacitor of capacitance \(C\), carrying total branch current \(I_2\). Which of the following correctly indicates the current \(I_1\) immediately after switch \(S\) is closed, the current \(I_2\) immediately after switch \(S\) is closed, and the current \(I_2\) a long time after switch \(S\) is closed?

![A rectangular circuit schematic in grayscale. On the left vertical branch is an ideal battery represented by two parallel horizontal plates, the longer upper plate labeled with a plus sign, labeled \(\mathcal{E}\). Above the battery on the top horizontal wire is an open single-pole switch labeled \(S\). The top wire extends rightward to a junction node. From this node, two parallel branches run downward to a bottom junction node that connects back to the negative terminal of the battery. The first branch, labeled with an arrow pointing downward labeled \(I_1\), contains a resistor labeled \(R\) in series with a capacitor of two equal-length parallel horizontal plates labeled \(C\). The second branch, labeled with a downward arrow labeled \(I_2\), contains an upper resistor labeled \(R\) connected in series with a parallel sub-loop; the left path of this sub-loop contains a resistor labeled \(R\) and the right path contains a capacitor labeled \(C\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1790604743-k3wDjp.jpg)

- **A.** | Current \(I_1\) at \(t = 0^+\) | Current \(I_2\) at \(t = 0^+\) | Current \(I_2\) as \(t \to \infty\) | | :---: | :---: | :---: | | \( \dfrac{\mathcal{E}}{R} \) | \( \dfrac{\mathcal{E}}{2R} \) | \( 0 \) |
- **B.** | Current \(I_1\) at \(t = 0^+\) | Current \(I_2\) at \(t = 0^+\) | Current \(I_2\) as \(t \to \infty\) | | :---: | :---: | :---: | | \( \dfrac{\mathcal{E}}{R} \) | \( \dfrac{\mathcal{E}}{R} \) | \( \dfrac{\mathcal{E}}{2R} \) |
- **C.** | Current \(I_1\) at \(t = 0^+\) | Current \(I_2\) at \(t = 0^+\) | Current \(I_2\) as \(t \to \infty\) | | :---: | :---: | :---: | | \( \dfrac{\mathcal{E}}{R} \) | \( \dfrac{\mathcal{E}}{R} \) | \( 0 \) |
- **D.** | Current \(I_1\) at \(t = 0^+\) | Current \(I_2\) at \(t = 0^+\) | Current \(I_2\) as \(t \to \infty\) | | :---: | :---: | :---: | | \( 0 \) | \( \dfrac{\mathcal{E}}{2R} \) | \( \dfrac{\mathcal{E}}{R} \) |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124972/*