---
title: "A capacitor with capacitance \\(C = 50\\text{ }\\mu\\text{F}\\) is initially charged and then discharged through a resistor of unknown resistance \\(R\\). A sensor records the current \\(I\\) in the circuit as a function of time \\(t\\), and a plot of \\(\\ln(I / \\text{A})\\) versus \\(t\\) is shown. Based on the graph, what is the resistance \\(R\\) of the resistor?"
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url: "https://nerd-notes.com/ubq/121583/"
date_modified: "2026-08-23T05:24:09+00:00"
---

# A capacitor with capacitance \(C = 50\text{ }\mu\text{F}\) is initially charged and then discharged through a resistor of unknown resistance \(R\). A sensor records the current \(I\) in the circuit as a function of time \(t\), and a plot of \(\ln(I / \text{A})\) versus \(t\) is shown. Based on the graph, what is the resistance \(R\) of the resistor?

A capacitor with capacitance \(C = 50\text{ }\mu\text{F}\) is initially charged and then discharged through a resistor of unknown resistance \(R\). A sensor records the current \(I\) in the circuit as a function of time \(t\), and a plot of \(\ln(I / \text{A})\) versus \(t\) is shown. Based on the graph, what is the resistance \(R\) of the resistor?

![A 2D Cartesian graph with gridlines. The horizontal axis is labeled t (s) and has major tick marks labeled 0, 2.0, 4.0, 6.0, 8.0. The vertical axis is labeled \ln(I / \text{A}) and has major tick marks labeled 0, -1.0, -2.0, -3.0, -4.0, -5.0, -6.0. Light gray gridlines extend across the plot area corresponding to every tick mark. A straight solid line with negative slope passes exactly through the grid intersections at (0, -2.0), (2.0, -3.0), (4.0, -4.0), (6.0, -5.0), and (8.0, -6.0). Black circular data points are plotted at each of these five grid intersections. No other labels, lines, text, or curves appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462649-yeFjOv.jpg)

- **A.** \(10\text{ k}\Omega\)
- **B.** \(20\text{ k}\Omega\)
- **C.** \(40\text{ k}\Omega\)
- **D.** \(80\text{ k}\Omega\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121583/*