---
title: "An electrical circuit consists of an ideal battery of emf \\(\\mathcal{E}\\), an open switch \\(S\\), two identical resistors of resistance \\(R_1 = R_2 = R\\), and an initially uncharged capacitor of capacitance \\(C\\), arranged as shown in the diagram. At time \\(t = 0\\), the switch \\(S\\) is closed.  Which of the following graphs best represents the electric potential difference \\(\\Delta V_C\\) across the capacitor as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/120461/"
date_modified: "2026-08-23T04:34:51+00:00"
---

# An electrical circuit consists of an ideal battery of emf \(\mathcal{E}\), an open switch \(S\), two identical resistors of resistance \(R_1 = R_2 = R\), and an initially uncharged capacitor of capacitance \(C\), arranged as shown in the diagram. At time \(t = 0\), the switch \(S\) is closed.

Which of the following graphs best represents the electric potential difference \(\Delta V_C\) across the capacitor as a function of time \(t\)?

An electrical circuit consists of an ideal battery of emf \(\mathcal{E}\), an open switch \(S\), two identical resistors of resistance \(R_1 = R_2 = R\), and an initially uncharged capacitor of capacitance \(C\), arranged as shown in the diagram. At time \(t = 0\), the switch \(S\) is closed.

Which of the following graphs best represents the electric potential difference \(\Delta V_C\) across the capacitor as a function of time \(t\)?

![Grayscale schematic diagram of a direct-current circuit. A rectangular outer loop has an ideal battery labeled \(\mathcal{E}\) on the left vertical wire, oriented with the longer positive plate on top. On the top horizontal wire, an open single-pole single-throw switch labeled \(S\) is followed in series by a zigzag resistor symbol labeled \(R_1\). To the right of \(R_1\), the circuit splits into two parallel vertical branches. The inner vertical branch contains a zigzag resistor symbol labeled \(R_2\). The outer vertical branch contains a capacitor symbol with two parallel plates labeled \(C\). The bottom horizontal wire connects the parallel branches back to the negative terminal of the battery. No other labels, meters, or arrows appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459689-tjCb8o.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120461/*