---
title: "An uncharged capacitor is connected in series with a resistor, an ideal battery with potential difference \\(V_0 = 10\\text{ V}\\), and an open switch. At time \\(t = 0\\), the switch is closed. The graph shows the measured potential difference \\(V_C\\) across the capacitor as a function of time \\(t\\) in milliseconds. The potential difference asymptotically approaches \\(10\\text{ V}\\), reaching \\(5.0\\text{ V}\\) at \\(t = 2.8\\text{ ms}\\) and \\(6.3\\text{ V}\\) at \\(t = 4.0\\text{ ms}\\). Based on the graph, what is the time constant \\(\\tau\\) of the circuit?"
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url: "https://nerd-notes.com/ubq/118381/"
date_modified: "2026-08-04T08:09:48+00:00"
---

# An uncharged capacitor is connected in series with a resistor, an ideal battery with potential difference \(V_0 = 10\text{ V}\), and an open switch. At time \(t = 0\), the switch is closed. The graph shows the measured potential difference \(V_C\) across the capacitor as a function of time \(t\) in milliseconds. The potential difference asymptotically approaches \(10\text{ V}\), reaching \(5.0\text{ V}\) at \(t = 2.8\text{ ms}\) and \(6.3\text{ V}\) at \(t = 4.0\text{ ms}\). Based on the graph, what is the time constant \(\tau\) of the circuit?

An uncharged capacitor is connected in series with a resistor, an ideal battery with potential difference \(V_0 = 10\text{ V}\), and an open switch. At time \(t = 0\), the switch is closed. The graph shows the measured potential difference \(V_C\) across the capacitor as a function of time \(t\) in milliseconds. The potential difference asymptotically approaches \(10\text{ V}\), reaching \(5.0\text{ V}\) at \(t = 2.8\text{ ms}\) and \(6.3\text{ V}\) at \(t = 4.0\text{ ms}\). Based on the graph, what is the time constant \(\tau\) of the circuit?

![A quantitative line graph showing capacitor potential difference V_C in volts on the vertical axis versus time t in milliseconds on the horizontal axis. The vertical axis ranges from 0 to 10 V with grid lines and tick marks labeled 0, 2, 4, 6, 8, 10. The horizontal axis ranges from 0 to 12 ms with grid lines and tick marks labeled 0, 2, 4, 6, 8, 10, 12. A horizontal dashed line is drawn at V_C = 10 V. A smooth continuous solid curve starts at (0, 0), rises smoothly, passing through (2.8 ms, 5.0 V) and (4.0 ms, 6.3 V), and asymptotically approaches V_C = 10 V. Dashed vertical and horizontal guidelines connect t = 4.0 ms on the time axis to V_C = 6.3 V on the potential axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830988-90eDhQ.jpg)

- **A.** \(1.0\text{ ms}\)
- **B.** \(2.0\text{ ms}\)
- **C.** \(2.8\text{ ms}\)
- **D.** \(4.0\text{ ms}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118381/*