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title: "A single-loop circuit consists of an ideal battery of potential difference \\(V_0\\), a resistor of resistance \\(R\\), an ideal inductor of inductance \\(L\\), and an open switch \\(S\\), all connected in series. The switch \\(S\\) has been open for a long time so that there is initially no current in the circuit. At time \\(t = 0\\), switch \\(S\\) is closed. Which of the following pairs correctly gives the current in the circuit immediately after switch \\(S\\) is closed (\\(t = 0\\)) and a long time after switch \\(S\\) is closed (\\(t \\to \\infty\\))?"
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url: "https://nerd-notes.com/ubq/118661/"
date_modified: "2026-08-04T08:13:35+00:00"
---

# A single-loop circuit consists of an ideal battery of potential difference \(V_0\), a resistor of resistance \(R\), an ideal inductor of inductance \(L\), and an open switch \(S\), all connected in series. The switch \(S\) has been open for a long time so that there is initially no current in the circuit. At time \(t = 0\), switch \(S\) is closed. Which of the following pairs correctly gives the current in the circuit immediately after switch \(S\) is closed (\(t = 0\)) and a long time after switch \(S\) is closed (\(t \to \infty\))?

A single-loop circuit consists of an ideal battery of potential difference \(V_0\), a resistor of resistance \(R\), an ideal inductor of inductance \(L\), and an open switch \(S\), all connected in series. The switch \(S\) has been open for a long time so that there is initially no current in the circuit. At time \(t = 0\), switch \(S\) is closed. Which of the following pairs correctly gives the current in the circuit immediately after switch \(S\) is closed (\(t = 0\)) and a long time after switch \(S\) is closed (\(t \to \infty\))?

![A schematic diagram of a single-loop electric circuit. On the left vertical branch is a DC battery labeled V_0, with the positive terminal on top indicated by a longer horizontal line and the negative terminal on bottom. The top horizontal branch contains an open switch labeled S. The right vertical branch contains a resistor drawn as a zig-zag line, labeled R. The bottom horizontal branch contains an inductor drawn as a series of four connected semi-circular loops, labeled L. Wires form a complete rectangular loop connecting all four components in series. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831215-SBjC8H.jpg)

- **A.** Immediately after: \(0\) ; A long time after: \(\dfrac{V_0}{R}\)
- **B.** Immediately after: \(\dfrac{V_0}{R}\) ; A long time after: \(0\)
- **C.** Immediately after: \(0\) ; A long time after: \(0\)
- **D.** Immediately after: \(\dfrac{V_0}{R}\) ; A long time after: \(\dfrac{V_0}{R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118661/*