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title: "A series circuit contains an ideal battery of electromotive force \\(\\mathcal{E}\\), an open switch \\(S\\), a resistor of resistance \\(R\\), and an uncharged capacitor of capacitance \\(C\\), as shown in the diagram. At time \\(t = 0\\), switch \\(S\\) is closed. Which of the following correctly pairs the current through the circuit immediately after the switch is closed (\\(t = 0^+\\)) and a long time after the switch is closed (\\(t \\to \\infty\\))?"
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url: "https://nerd-notes.com/ubq/121557/"
date_modified: "2026-08-23T05:24:00+00:00"
---

# A series circuit contains an ideal battery of electromotive force \(\mathcal{E}\), an open switch \(S\), a resistor of resistance \(R\), and an uncharged capacitor of capacitance \(C\), as shown in the diagram. At time \(t = 0\), switch \(S\) is closed. Which of the following correctly pairs the current through the circuit immediately after the switch is closed (\(t = 0^+\)) and a long time after the switch is closed (\(t \to \infty\))?

A series circuit contains an ideal battery of electromotive force \(\mathcal{E}\), an open switch \(S\), a resistor of resistance \(R\), and an uncharged capacitor of capacitance \(C\), as shown in the diagram. At time \(t = 0\), switch \(S\) is closed. Which of the following correctly pairs the current through the circuit immediately after the switch is closed (\(t = 0^+\)) and a long time after the switch is closed (\(t \to \infty\))?

![A single-loop rectangular circuit diagram oriented horizontally. On the left vertical branch is a battery symbol with EMF label \(\mathcal{E}\), with the longer positive plate on top. On the top horizontal branch is a switch symbol in the open position labeled \(S\). On the right vertical branch is a resistor symbol labeled \(R\). On the bottom horizontal branch is a parallel-plate capacitor symbol labeled \(C\). Thin solid lines connect all four components into a single rectangular loop. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-rc-circuit-1787462640-pCOSvz.jpg)

- **A.** \(I(0^+) = \dfrac{\mathcal{E}}{R}\) and \(I(\infty) = 0\)
- **B.** \(I(0^+) = \dfrac{\mathcal{E}}{R}\) and \(I(\infty) = \dfrac{\mathcal{E}}{R}\)
- **C.** \(I(0^+) = 0\) and \(I(\infty) = \dfrac{\mathcal{E}}{R}\)
- **D.** \(I(0^+) = 0\) and \(I(\infty) = 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121557/*