---
title: "Two separate circuits each contain an ideal battery of electromotive force \\(\\mathcal{E}\\), an open switch, a resistor of resistance \\(R\\), and an initially uncharged parallel-plate capacitor. Capacitor 1 has capacitance \\(C_1\\) and Capacitor 2 has capacitance \\(C_2\\). At time \\(t = 0\\), both switches are closed, and the potential difference \\(V(t)\\) across each capacitor is recorded as a function of time \\(t\\), as shown in the graph. Which of the following statements correctly compares the capacitances of the two capacitors and their initial displacement currents \\(I_d = \\varepsilon_0 \\dfrac{d\\Phi_E}{dt}\\) at \\(t = 0\\)?"
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url: "https://nerd-notes.com/ubq/124910/"
date_modified: "2026-09-28T14:11:55+00:00"
---

# Two separate circuits each contain an ideal battery of electromotive force \(\mathcal{E}\), an open switch, a resistor of resistance \(R\), and an initially uncharged parallel-plate capacitor. Capacitor 1 has capacitance \(C_1\) and Capacitor 2 has capacitance \(C_2\). At time \(t = 0\), both switches are closed, and the potential difference \(V(t)\) across each capacitor is recorded as a function of time \(t\), as shown in the graph. Which of the following statements correctly compares the capacitances of the two capacitors and their initial displacement currents \(I_d = \varepsilon_0 \dfrac{d\Phi_E}{dt}\) at \(t = 0\)?

Two separate circuits each contain an ideal battery of electromotive force \(\mathcal{E}\), an open switch, a resistor of resistance \(R\), and an initially uncharged parallel-plate capacitor. Capacitor 1 has capacitance \(C_1\) and Capacitor 2 has capacitance \(C_2\). At time \(t = 0\), both switches are closed, and the potential difference \(V(t)\) across each capacitor is recorded as a function of time \(t\), as shown in the graph. Which of the following statements correctly compares the capacitances of the two capacitors and their initial displacement currents \(I_d = \varepsilon_0 \dfrac{d\Phi_E}{dt}\) at \(t = 0\)?

![A Cartesian graph with a horizontal axis labeled t and a vertical axis labeled V(t). The axes meet at an origin labeled 0. There are no gridlines. A horizontal dotted line extends to the right from the vertical axis at a positive value labeled \(\mathcal{E}\). Two concave-down curves begin at the origin (0,0) and approach the dotted line asymptotically from below. The first curve is a solid line labeled 'Curve 1' that rises steeply near the origin and flattens out near the dotted line. The second curve is a dashed line labeled 'Curve 2' that rises with a shallower initial slope than the first curve and approaches the dotted line more gradually. The solid curve remains above the dashed curve for all positive values of t. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-graph-1-1790604714-XsYPL3.jpg)

- **A.** \(C_1 < C_2\), and the initial displacement currents satisfy \(I_{d,1}(0) = I_{d,2}(0)\).
- **B.** \(C_1 > C_2\), and the initial displacement currents satisfy \(I_{d,1}(0) > I_{d,2}(0)\).
- **C.** \(C_1 < C_2\), and the initial displacement currents satisfy \(I_{d,1}(0) > I_{d,2}(0)\).
- **D.** \(C_1 > C_2\), and the initial displacement currents satisfy \(I_{d,1}(0) = I_{d,2}(0)\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124910/*