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title: "An experiment is performed to determine the unknown self-inductance \\(L\\) of an inductor using an ideal \\(LC\\) circuit. The inductor is connected in series with a decade capacitance box of variable capacitance \\(C\\), and the period \\(T\\) of electromagnetic oscillations is measured for several values of \\(C\\). To determine \\(L\\) from a linear graph whose slope is directly proportional to \\(L\\), which quantities should be plotted on the vertical and horizontal axes, and what is the expected slope of the best-fit line?"
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url: "https://nerd-notes.com/ubq/125004/"
date_modified: "2026-09-28T14:13:07+00:00"
---

# An experiment is performed to determine the unknown self-inductance \(L\) of an inductor using an ideal \(LC\) circuit. The inductor is connected in series with a decade capacitance box of variable capacitance \(C\), and the period \(T\) of electromagnetic oscillations is measured for several values of \(C\). To determine \(L\) from a linear graph whose slope is directly proportional to \(L\), which quantities should be plotted on the vertical and horizontal axes, and what is the expected slope of the best-fit line?

An experiment is performed to determine the unknown self-inductance \(L\) of an inductor using an ideal \(LC\) circuit. The inductor is connected in series with a decade capacitance box of variable capacitance \(C\), and the period \(T\) of electromagnetic oscillations is measured for several values of \(C\). To determine \(L\) from a linear graph whose slope is directly proportional to \(L\), which quantities should be plotted on the vertical and horizontal axes, and what is the expected slope of the best-fit line?

![A single rectangular circuit schematic oriented with horizontal top and bottom branches and vertical left and right branches. The left vertical branch contains an inductor drawn as four adjacent semicircular loops, labeled L to its left. The right vertical branch contains a variable capacitor drawn as two parallel horizontal line segments separated by a small gap, with a single diagonal arrow passing through the center of the plates pointing toward the upper-right, labeled C to its right. The top and bottom branches are straight solid conducting wires connecting the inductor and capacitor to form a single closed loop. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604786-Fkj9Yc.jpg)

- **A.** Vertical axis: \(T^2\) Horizontal axis: \(C\) Slope: \(4\pi^2 L\)
- **B.** Vertical axis: \(T^2\) Horizontal axis: \(C\) Slope: \(\dfrac{L}{4\pi^2}\)
- **C.** Vertical axis: \(C\) Horizontal axis: \(T^2\) Slope: \(\dfrac{1}{4\pi^2 L}\)
- **D.** Vertical axis: \(T\) Horizontal axis: \(\sqrt{C}\) Slope: \(2\pi L\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125004/*