---
title: "Circuit 1 consists of a resistor of resistance \\(R\\) and an uncharged capacitor of capacitance \\(C\\) connected in series to an ideal battery of potential difference \\(V_0\\). Circuit 2 consists of a resistor of resistance \\(2R\\) and an uncharged capacitor of capacitance \\(C\\) connected in series to an identical battery. At time \\(t = 0\\), switches in both circuits are closed to begin charging the capacitors. Let \\(t_1\\) and \\(t_2\\) be the times required for the capacitors in Circuit 1 and Circuit 2, respectively, to reach half of their maximum charge. Which of the following correctly compares \\(t_1\\) and \\(t_2\\), and describes the shape of the charge versus time graph \\(q(t)\\) during charging?"
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url: "https://nerd-notes.com/ubq/118421/"
date_modified: "2026-08-04T08:10:00+00:00"
---

# Circuit 1 consists of a resistor of resistance \(R\) and an uncharged capacitor of capacitance \(C\) connected in series to an ideal battery of potential difference \(V_0\). Circuit 2 consists of a resistor of resistance \(2R\) and an uncharged capacitor of capacitance \(C\) connected in series to an identical battery. At time \(t = 0\), switches in both circuits are closed to begin charging the capacitors. Let \(t_1\) and \(t_2\) be the times required for the capacitors in Circuit 1 and Circuit 2, respectively, to reach half of their maximum charge. Which of the following correctly compares \(t_1\) and \(t_2\), and describes the shape of the charge versus time graph \(q(t)\) during charging?

Circuit 1 consists of a resistor of resistance \(R\) and an uncharged capacitor of capacitance \(C\) connected in series to an ideal battery of potential difference \(V_0\). Circuit 2 consists of a resistor of resistance \(2R\) and an uncharged capacitor of capacitance \(C\) connected in series to an identical battery. At time \(t = 0\), switches in both circuits are closed to begin charging the capacitors. Let \(t_1\) and \(t_2\) be the times required for the capacitors in Circuit 1 and Circuit 2, respectively, to reach half of their maximum charge. Which of the following correctly compares \(t_1\) and \(t_2\), and describes the shape of the charge versus time graph \(q(t)\) during charging?

- **A.** \(t_1 > t_2\), and the graph of \(q(t)\) is concave upward.
- **B.** \(t_1 > t_2\), and the graph of \(q(t)\) is concave downward.
- **C.** \(t_1 < t_2\), and the graph of \(q(t)\) is concave upward.
- **D.** \(t_1 < t_2\), and the graph of \(q(t)\) is concave downward.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118421/*