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title: "A parallel-plate capacitor with plate area \\(A\\) and initial plate separation \\(x_0\\) is connected in series with an ideal battery of potential difference \\(\\mathcal{E}\\) and a resistor of resistance \\(R\\). The system has been connected for a long time so that the capacitor is fully charged. Beginning at time \\(t = 0\\), an external mechanism pulls one plate away from the other at a constant speed \\(v\\), increasing the plate separation according to \\(x(t) = x_0 + vt\\). Which of the following best describes the shape of the graph of the current \\(I(t)\\) through the resistor as a function of time \\(t\\) for \\(t \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/124894/"
date_modified: "2026-09-28T14:11:51+00:00"
---

# A parallel-plate capacitor with plate area \(A\) and initial plate separation \(x_0\) is connected in series with an ideal battery of potential difference \(\mathcal{E}\) and a resistor of resistance \(R\). The system has been connected for a long time so that the capacitor is fully charged. Beginning at time \(t = 0\), an external mechanism pulls one plate away from the other at a constant speed \(v\), increasing the plate separation according to \(x(t) = x_0 + vt\). Which of the following best describes the shape of the graph of the current \(I(t)\) through the resistor as a function of time \(t\) for \(t \ge 0\)?

A parallel-plate capacitor with plate area \(A\) and initial plate separation \(x_0\) is connected in series with an ideal battery of potential difference \(\mathcal{E}\) and a resistor of resistance \(R\). The system has been connected for a long time so that the capacitor is fully charged. Beginning at time \(t = 0\), an external mechanism pulls one plate away from the other at a constant speed \(v\), increasing the plate separation according to \(x(t) = x_0 + vt\). Which of the following best describes the shape of the graph of the current \(I(t)\) through the resistor as a function of time \(t\) for \(t \ge 0\)?

![A single-loop rectangular circuit diagram drawn in black and white. On the left vertical branch is a DC voltage source labeled \(\mathcal{E}\), with the longer horizontal bar on top indicating the positive terminal and the shorter bar on the bottom indicating the negative terminal. The top horizontal wire contains a standard zig-zag resistor labeled \(R\). The right vertical branch contains a parallel-plate capacitor consisting of two identical, parallel vertical line segments of equal height. The left plate is fixed in position. The right plate has a single horizontal arrow pointing to the right labeled \(v\), indicating motion away from the left plate. A double-headed horizontal dimension arrow between the two plates is labeled \(x(t)\). Straight conducting wire segments connect the components to form a closed rectangular loop. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604710-plOtzy.jpg)

- **A.** Starts at a non-zero maximum value at \(t = 0\) and decreases monotonically toward zero as \(t \to \infty\).
- **B.** Starts at a non-zero value at \(t = 0\) and remains constant for all \(t > 0\).
- **C.** Starts at zero at \(t = 0\), increases to a maximum value, and then asymptotically decreases toward zero as \(t \to \infty\).
- **D.** Starts at zero at \(t = 0\) and increases monotonically toward a non-zero horizontal asymptote as \(t \to \infty\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124894/*