---
title: "A circuit consists of an ideal battery with an emf of \\(\\varepsilon = 12\\text{ V}\\), an open switch, a resistor of resistance \\(R\\), and an inductor of self-inductance \\(L\\) connected in series.  At time \\(t = 0\\), the switch is closed, and the current \\(I\\) in the circuit is recorded as a function of time \\(t\\), as shown in the graph. A dashed tangent line to the curve at \\(t = 0\\) is drawn, along with a dashed horizontal line indicating the steady-state current.  Based on the graph, what is the self-inductance \\(L\\) of the inductor?"
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url: "https://nerd-notes.com/ubq/125026/"
date_modified: "2026-09-28T14:13:20+00:00"
---

# A circuit consists of an ideal battery with an emf of \(\varepsilon = 12\text{ V}\), an open switch, a resistor of resistance \(R\), and an inductor of self-inductance \(L\) connected in series.

At time \(t = 0\), the switch is closed, and the current \(I\) in the circuit is recorded as a function of time \(t\), as shown in the graph. A dashed tangent line to the curve at \(t = 0\) is drawn, along with a dashed horizontal line indicating the steady-state current.

Based on the graph, what is the self-inductance \(L\) of the inductor?

A circuit consists of an ideal battery with an emf of \(\varepsilon = 12\text{ V}\), an open switch, a resistor of resistance \(R\), and an inductor of self-inductance \(L\) connected in series.

At time \(t = 0\), the switch is closed, and the current \(I\) in the circuit is recorded as a function of time \(t\), as shown in the graph. A dashed tangent line to the curve at \(t = 0\) is drawn, along with a dashed horizontal line indicating the steady-state current.

Based on the graph, what is the self-inductance \(L\) of the inductor?

![A two-dimensional Cartesian graph with a horizontal axis labeled \(t\text{ (s)}\) and a vertical axis labeled \(I\text{ (A)}\). The horizontal axis has tick marks and numerical labels at \(0\), \(0.5\), \(1.0\), \(1.5\), and \(2.0\). The vertical axis has tick marks and numerical labels at \(0\), \(0.5\), \(1.0\), \(1.5\), \(2.0\), and \(2.5\). Thin gray gridlines extend across the plot. A solid black curve begins at the origin \((0, 0)\), curves concave-downward, and asymptotically approaches a horizontal dashed line at \(I = 2.0\text{ A}\). A straight dashed line starts at the origin \((0, 0)\), is tangent to the solid curve at the origin, and passes directly through the coordinate point \((0.5, 2.0)\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604800-kD5NzO.jpg)

- **A.** \(0.50\text{ H}\)
- **B.** \(3.0\text{ H}\)
- **C.** \(6.0\text{ H}\)
- **D.** \(12\text{ H}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125026/*