---
title: "A single-loop circuit contains an ideal battery of emf \\(\\mathcal{E}\\), an open switch \\(S\\), a resistor of resistance \\(R\\), and an inductor of inductance \\(L\\), as shown in the diagram. At time \\(t = 0\\), switch \\(S\\) is closed.  Which row in the table correctly identifies the current in the circuit immediately after the switch is closed (at \\(t = 0^+\\)) and the inductive time constant \\(\\tau\\) of the circuit?  | Row | Current at \\(t = 0^+\\) | Inductive time constant \\(\\tau\\) | | :— | :— | :— | | Row A | \\(\\dfrac{\\mathcal{E}}{R}\\) | \\(\\dfrac{R}{L}\\) | | Row B | \\(\\dfrac{\\mathcal{E}}{R}\\) | \\(\\dfrac{L}{R}\\) | | Row C | \\(0\\) | \\(\\dfrac{L}{R}\\) | | Row D | \\(0\\) | \\(\\dfrac{R}{L}\\) |"
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url: "https://nerd-notes.com/ubq/121315/"
date_modified: "2026-08-23T04:59:41+00:00"
---

# A single-loop circuit contains an ideal battery of emf \(\mathcal{E}\), an open switch \(S\), a resistor of resistance \(R\), and an inductor of inductance \(L\), as shown in the diagram. At time \(t = 0\), switch \(S\) is closed.

Which row in the table correctly identifies the current in the circuit immediately after the switch is closed (at \(t = 0^+\)) and the inductive time constant \(\tau\) of the circuit?

| Row | Current at \(t = 0^+\) | Inductive time constant \(\tau\) |
| :— | :— | :— |
| Row A | \(\dfrac{\mathcal{E}}{R}\) | \(\dfrac{R}{L}\) |
| Row B | \(\dfrac{\mathcal{E}}{R}\) | \(\dfrac{L}{R}\) |
| Row C | \(0\) | \(\dfrac{L}{R}\) |
| Row D | \(0\) | \(\dfrac{R}{L}\) |

A single-loop circuit contains an ideal battery of emf \(\mathcal{E}\), an open switch \(S\), a resistor of resistance \(R\), and an inductor of inductance \(L\), as shown in the diagram. At time \(t = 0\), switch \(S\) is closed.

Which row in the table correctly identifies the current in the circuit immediately after the switch is closed (at \(t = 0^+\)) and the inductive time constant \(\tau\) of the circuit?

| Row | Current at \(t = 0^+\) | Inductive time constant \(\tau\) |
| :--- | :--- | :--- |
| Row A | \(\dfrac{\mathcal{E}}{R}\) | \(\dfrac{R}{L}\) |
| Row B | \(\dfrac{\mathcal{E}}{R}\) | \(\dfrac{L}{R}\) |
| Row C | \(0\) | \(\dfrac{L}{R}\) |
| Row D | \(0\) | \(\dfrac{R}{L}\) |

![A single rectangular circuit loop oriented with horizontal top and bottom wires and vertical left and right wires. On the left vertical segment is an ideal DC battery symbol labeled \(\mathcal{E}\), with the longer positive plate on top. On the top horizontal segment is an open switch labeled \(S\). On the right vertical segment is a zig-zag resistor symbol labeled \(R\). On the bottom horizontal segment is a series of four rounded coiled loops representing an inductor labeled \(L\). All four components are connected in series by solid straight wire segments forming a closed perimeter when the switch is closed. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461180-LYh3W3.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121315/*