---
title: "A capacitor of unknown capacitance \\(C\\) is initially charged to a potential difference \\(V_0\\) and then allowed to discharge through a resistor of known resistance \\(R\\). A student records the potential difference \\(V\\) across the capacitor as a function of elapsed time \\(t\\) using a voltmeter with a known, finite internal resistance \\(R_V\\) connected in parallel with the capacitor. To determine \\(C\\), the student linearizes the data by plotting \\(\\ln V\\) on the vertical axis versus \\(t\\) on the horizontal axis, obtaining a best-fit line with a slope of magnitude \\(S\\). Which of the following expressions correctly yields the capacitance \\(C\\) in terms of \\(S\\), \\(R\\), and \\(R_V\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/124994/"
date_modified: "2026-09-28T14:12:50+00:00"
---

# A capacitor of unknown capacitance \(C\) is initially charged to a potential difference \(V_0\) and then allowed to discharge through a resistor of known resistance \(R\). A student records the potential difference \(V\) across the capacitor as a function of elapsed time \(t\) using a voltmeter with a known, finite internal resistance \(R_V\) connected in parallel with the capacitor. To determine \(C\), the student linearizes the data by plotting \(\ln V\) on the vertical axis versus \(t\) on the horizontal axis, obtaining a best-fit line with a slope of magnitude \(S\). Which of the following expressions correctly yields the capacitance \(C\) in terms of \(S\), \(R\), and \(R_V\)?

A capacitor of unknown capacitance \(C\) is initially charged to a potential difference \(V_0\) and then allowed to discharge through a resistor of known resistance \(R\). A student records the potential difference \(V\) across the capacitor as a function of elapsed time \(t\) using a voltmeter with a known, finite internal resistance \(R_V\) connected in parallel with the capacitor. To determine \(C\), the student linearizes the data by plotting \(\ln V\) on the vertical axis versus \(t\) on the horizontal axis, obtaining a best-fit line with a slope of magnitude \(S\). Which of the following expressions correctly yields the capacitance \(C\) in terms of \(S\), \(R\), and \(R_V\)?

![A rectangular circuit schematic drawn in grayscale lines. On the left vertical branch sits a capacitor symbol labeled C. The top and bottom horizontal wires connect this left branch to a central vertical branch containing a resistor symbol labeled R. Extending further to the right, the top and bottom wires continue to form a parallel right vertical branch containing a circle with a capital letter V inside, labeled as having internal resistance R_V. A closed switch symbol is shown on the top wire between the capacitor and the central resistor branch. Direction arrows are omitted. All wire lines are solid black on a white background. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604770-M7t8pz.jpg)

- **A.** \(C = \dfrac{1}{S R}\)
- **B.** \(C = \dfrac{1}{S(R + R_V)}\)
- **C.** \(C = \dfrac{R_V}{S R (R + R_V)}\)
- **D.** \(C = \dfrac{R + R_V}{S R R_V}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124994/*