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title: "A circuit is constructed using an ideal battery of electromotive force \\(\\mathcal{E}\\), four resistors, and an initially uncharged capacitor of capacitance \\(C\\). Two parallel branches connect the terminals of the battery: the first branch contains a resistor of resistance \\(R\\) in series with a resistor of resistance \\(3R\\) meeting at junction \\(X\\), and the second branch contains a resistor of resistance \\(3R\\) in series with a resistor of resistance \\(R\\) meeting at junction \\(Y\\). The capacitor connects junction \\(X\\) directly to junction \\(Y\\). After the circuit has reached a steady state, which of the following correctly identifies the potential difference across the capacitor and the plate that is at a higher electric potential?"
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url: "https://nerd-notes.com/ubq/124773/"
date_modified: "2026-09-28T14:11:12+00:00"
---

# A circuit is constructed using an ideal battery of electromotive force \(\mathcal{E}\), four resistors, and an initially uncharged capacitor of capacitance \(C\). Two parallel branches connect the terminals of the battery: the first branch contains a resistor of resistance \(R\) in series with a resistor of resistance \(3R\) meeting at junction \(X\), and the second branch contains a resistor of resistance \(3R\) in series with a resistor of resistance \(R\) meeting at junction \(Y\). The capacitor connects junction \(X\) directly to junction \(Y\). After the circuit has reached a steady state, which of the following correctly identifies the potential difference across the capacitor and the plate that is at a higher electric potential?

A circuit is constructed using an ideal battery of electromotive force \(\mathcal{E}\), four resistors, and an initially uncharged capacitor of capacitance \(C\). Two parallel branches connect the terminals of the battery: the first branch contains a resistor of resistance \(R\) in series with a resistor of resistance \(3R\) meeting at junction \(X\), and the second branch contains a resistor of resistance \(3R\) in series with a resistor of resistance \(R\) meeting at junction \(Y\). The capacitor connects junction \(X\) directly to junction \(Y\). After the circuit has reached a steady state, which of the following correctly identifies the potential difference across the capacitor and the plate that is at a higher electric potential?

![A circuit schematic with rectangular wire loops. On the far left, a vertical branch contains a DC battery with a long upper horizontal plate labeled with a plus sign and a shorter lower plate, labeled \(\mathcal{E}\). Wires extend horizontally to the right from the top and bottom terminals of the battery to connect two vertical parallel branches. The first vertical branch contains an upper resistor labeled \(R\), a central junction labeled \(X\), and a lower resistor labeled \(3R\). The second vertical branch, positioned to the right of the first, contains an upper resistor labeled \(3R\), a central junction labeled \(Y\), and a lower resistor labeled \(R\). A horizontal cross-branch connects junction \(X\) and junction \(Y\), containing a capacitor with two equal vertical parallel plates labeled \(C\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604672-cIZQN5.jpg)

- **A.** \(\Delta V_C = \dfrac{1}{2}\mathcal{E}\) ; Plate connected to junction \(X\)
- **B.** \(\Delta V_C = \dfrac{1}{2}\mathcal{E}\) ; Plate connected to junction \(Y\)
- **C.** \(\Delta V_C = \dfrac{1}{4}\mathcal{E}\) ; Plate connected to junction \(X\)
- **D.** \(\Delta V_C = \dfrac{1}{4}\mathcal{E}\) ; Plate connected to junction \(Y\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124773/*