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title: "Three initially uncharged capacitors of capacitance \\(C\\), \\(2C\\), and \\(3C\\) are connected in series across an ideal battery of potential difference \\(V_0\\). Let \\(\\Delta V_1\\), \\(\\Delta V_2\\), and \\(\\Delta V_3\\) represent the steady-state potential differences across capacitors \\(C\\), \\(2C\\), and \\(3C\\), respectively, and let \\(U_1\\), \\(U_2\\), and \\(U_3\\) represent their respective stored electrostatic energies.  Which of the following correctly ranks the potential differences and stored electrostatic energies for the three capacitors?"
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url: "https://nerd-notes.com/ubq/121119/"
date_modified: "2026-08-23T04:58:10+00:00"
---

# Three initially uncharged capacitors of capacitance \(C\), \(2C\), and \(3C\) are connected in series across an ideal battery of potential difference \(V_0\). Let \(\Delta V_1\), \(\Delta V_2\), and \(\Delta V_3\) represent the steady-state potential differences across capacitors \(C\), \(2C\), and \(3C\), respectively, and let \(U_1\), \(U_2\), and \(U_3\) represent their respective stored electrostatic energies.

Which of the following correctly ranks the potential differences and stored electrostatic energies for the three capacitors?

Three initially uncharged capacitors of capacitance \(C\), \(2C\), and \(3C\) are connected in series across an ideal battery of potential difference \(V_0\). Let \(\Delta V_1\), \(\Delta V_2\), and \(\Delta V_3\) represent the steady-state potential differences across capacitors \(C\), \(2C\), and \(3C\), respectively, and let \(U_1\), \(U_2\), and \(U_3\) represent their respective stored electrostatic energies.

Which of the following correctly ranks the potential differences and stored electrostatic energies for the three capacitors?

![A single rectangular circuit loop in grayscale. The left vertical branch contains an ideal battery labeled V_0 with standard long and short parallel plate symbols (long plate at top). The top horizontal branch contains three capacitors connected in series, spaced evenly: the first capacitor is labeled C, the middle capacitor is labeled 2C, and the third capacitor is labeled 3C. The bottom horizontal branch and right vertical branch are solid connecting wires. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461090-xIz60Q.jpg)

- **A.** \(\Delta V_1 < \Delta V_2 < \Delta V_3\) and \(U_1 < U_2 < U_3\)
- **B.** \(\Delta V_1 > \Delta V_2 > \Delta V_3\) and \(U_1 < U_2 < U_3\)
- **C.** \(\Delta V_1 > \Delta V_2 > \Delta V_3\) and \(U_1 > U_2 > U_3\)
- **D.** \(\Delta V_1 = \Delta V_2 = \Delta V_3\) and \(U_1 < U_2 < U_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121119/*