---
title: "An LC circuit consists of an inductor with inductance \\(L = 50\\text{ mH}\\) connected in series with a capacitor of unknown capacitance \\(C\\). The circuit undergoes undamped oscillations, and the resulting current \\(I\\) as a function of time \\(t\\) is displayed on an oscilloscope screen with a horizontal time scale of \\(1.0\\text{ ms}\\) per division, as shown in the graph. Based on the oscilloscope trace, what is the capacitance of the capacitor?"
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url: "https://nerd-notes.com/ubq/125065/"
date_modified: "2026-09-28T14:14:24+00:00"
---

# An LC circuit consists of an inductor with inductance \(L = 50\text{ mH}\) connected in series with a capacitor of unknown capacitance \(C\). The circuit undergoes undamped oscillations, and the resulting current \(I\) as a function of time \(t\) is displayed on an oscilloscope screen with a horizontal time scale of \(1.0\text{ ms}\) per division, as shown in the graph. Based on the oscilloscope trace, what is the capacitance of the capacitor?

An LC circuit consists of an inductor with inductance \(L = 50\text{ mH}\) connected in series with a capacitor of unknown capacitance \(C\). The circuit undergoes undamped oscillations, and the resulting current \(I\) as a function of time \(t\) is displayed on an oscilloscope screen with a horizontal time scale of \(1.0\text{ ms}\) per division, as shown in the graph. Based on the oscilloscope trace, what is the capacitance of the capacitor?

![A rectangular oscilloscope display with a grid of thin gray coordinate lines forming 8 horizontal divisions and 6 vertical divisions. A horizontal central axis is labeled t at its far right, with vertical tick marks spaced by 1 division, labeled from 0 at the left vertical axis to 6 at the sixth vertical grid line. A vertical central axis is labeled I at its top. A single solid sinusoidal curve begins at the origin (0, 0), passes through a crest at horizontal division 1 with a height of 2 vertical divisions above the central axis, crosses the horizontal axis downward at horizontal division 2, reaches a trough at horizontal division 3 with a depth of 2 vertical divisions below the central axis, crosses the horizontal axis upward at horizontal division 4, reaches a second identical crest at horizontal division 5, and crosses the horizontal axis downward at horizontal division 6. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604864-OA8s2K.jpg)

- **A.** \(2.0\text{ }\mu\text{F}\)
- **B.** \(8.1\text{ }\mu\text{F}\)
- **C.** \(32\text{ }\mu\text{F}\)
- **D.** \(320\text{ }\mu\text{F}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125065/*