---
title: "A student conducts an experiment to determine the time constant \\(\\tau\\) of an \\(LR\\) circuit consisting of an inductor of inductance \\(L\\) and a resistor of resistance \\(R\\). After a steady-state current \\(I_0\\) is established, the power source is removed at time \\(t = 0\\), and the current \\(I(t)\\) decays according to \\(I(t) = I_0 e^{-t/\\tau}\\), where \\(\\tau = \\dfrac{L}{R}\\). To obtain a linear graph from the experimental data, which quantities should the student plot on the vertical and horizontal axes, and how is the time constant \\(\\tau\\) determined from the slope \\(m\\) of the resulting best-fit line?"
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url: "https://nerd-notes.com/ubq/121320/"
date_modified: "2026-08-23T04:59:41+00:00"
---

# A student conducts an experiment to determine the time constant \(\tau\) of an \(LR\) circuit consisting of an inductor of inductance \(L\) and a resistor of resistance \(R\). After a steady-state current \(I_0\) is established, the power source is removed at time \(t = 0\), and the current \(I(t)\) decays according to \(I(t) = I_0 e^{-t/\tau}\), where \(\tau = \dfrac{L}{R}\). To obtain a linear graph from the experimental data, which quantities should the student plot on the vertical and horizontal axes, and how is the time constant \(\tau\) determined from the slope \(m\) of the resulting best-fit line?

A student conducts an experiment to determine the time constant \(\tau\) of an \(LR\) circuit consisting of an inductor of inductance \(L\) and a resistor of resistance \(R\). After a steady-state current \(I_0\) is established, the power source is removed at time \(t = 0\), and the current \(I(t)\) decays according to \(I(t) = I_0 e^{-t/\tau}\), where \(\tau = \dfrac{L}{R}\). To obtain a linear graph from the experimental data, which quantities should the student plot on the vertical and horizontal axes, and how is the time constant \(\tau\) determined from the slope \(m\) of the resulting best-fit line?

![A single rectangular closed circuit loop drawn in thin solid lines. The top horizontal wire contains an inductor symbol with four rounded bumps labeled \(L\). The right vertical wire contains a rectangular zigzag resistor symbol labeled \(R\). A current arrow labeled \(I(t)\) points clockwise along the bottom horizontal wire. No battery or switch appears. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461181-VviVIA.jpg)

- **A.** Plot \(\ln(I)\) on the vertical axis and \(t\) on the horizontal axis; \(\tau = -\dfrac{1}{m}\)
- **B.** Plot \(\ln(I)\) on the vertical axis and \(t\) on the horizontal axis; \(\tau = -m\)
- **C.** Plot \(\dfrac{1}{I}\) on the vertical axis and \(t\) on the horizontal axis; \(\tau = \dfrac{1}{m}\)
- **D.** Plot \(\dfrac{1}{I}\) on the vertical axis and \(t\) on the horizontal axis; \(\tau = -m\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121320/*