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title: "A capacitor with capacitance \\(C\\) is fully charged so that the potential difference across its plates is \\(\\Delta V_0\\). At time \\(t = 0\\), the capacitor is connected in a single closed loop containing an open switch and a resistor of resistance \\(R\\), and the switch is immediately closed. Which of the following best describes the graph of the magnitude of the current \\(I\\) through the resistor as a function of time \\(t\\) after the switch is closed?"
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url: "https://nerd-notes.com/ubq/120387/"
date_modified: "2026-08-23T04:34:26+00:00"
---

# A capacitor with capacitance \(C\) is fully charged so that the potential difference across its plates is \(\Delta V_0\). At time \(t = 0\), the capacitor is connected in a single closed loop containing an open switch and a resistor of resistance \(R\), and the switch is immediately closed. Which of the following best describes the graph of the magnitude of the current \(I\) through the resistor as a function of time \(t\) after the switch is closed?

A capacitor with capacitance \(C\) is fully charged so that the potential difference across its plates is \(\Delta V_0\). At time \(t = 0\), the capacitor is connected in a single closed loop containing an open switch and a resistor of resistance \(R\), and the switch is immediately closed. Which of the following best describes the graph of the magnitude of the current \(I\) through the resistor as a function of time \(t\) after the switch is closed?

![A single rectangular circuit schematic oriented horizontally. The left vertical branch contains a capacitor with two parallel horizontal plates labeled C. The right vertical branch contains a zigzag resistor labeled R. The top horizontal wire contains an open single-pole single-throw switch labeled S tilted upward at 30 degrees. The bottom wire is a continuous straight horizontal line connecting the bottom of the capacitor to the bottom of the resistor. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459665-uL1sZL.jpg)

- **A.** The graph begins at \(I = \dfrac{\Delta V_0}{R}\) and decreases linearly with a constant negative slope, reaching zero at time \(t = RC\).
- **B.** The graph begins at \(I = 0\) and increases nonlinearly with a decreasing slope, asymptotically approaching \(I = \dfrac{\Delta V_0}{R}\).
- **C.** The graph begins at \(I = \dfrac{\Delta V_0}{R}\) and decreases nonlinearly with an increasing magnitude of slope (concave downward), reaching zero at time \(t = RC\).
- **D.** The graph begins at \(I = \dfrac{\Delta V_0}{R}\) and decreases nonlinearly with a decreasing magnitude of slope (concave upward), asymptotically approaching zero and reaching approximately \(0.37\left(\dfrac{\Delta V_0}{R}\right)\) at time \(t = RC\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120387/*