---
title: "An ideal battery of electromotive force (EMF) \\(\\mathcal{E}\\) is connected to a capacitor of capacitance \\(C\\) through terminal 1 of a switch \\(S\\). After the capacitor has become fully charged, the switch is thrown at time \\(t = 0\\) to terminal 2, disconnecting the battery and connecting the capacitor directly across an ideal inductor of inductance \\(L\\). What are the peak current in the resulting circuit and the first elapsed time \\(t > 0\\) at which this peak current occurs?"
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url: "https://nerd-notes.com/ubq/125044/"
date_modified: "2026-09-28T14:13:37+00:00"
---

# An ideal battery of electromotive force (EMF) \(\mathcal{E}\) is connected to a capacitor of capacitance \(C\) through terminal 1 of a switch \(S\). After the capacitor has become fully charged, the switch is thrown at time \(t = 0\) to terminal 2, disconnecting the battery and connecting the capacitor directly across an ideal inductor of inductance \(L\). What are the peak current in the resulting circuit and the first elapsed time \(t > 0\) at which this peak current occurs?

An ideal battery of electromotive force (EMF) \(\mathcal{E}\) is connected to a capacitor of capacitance \(C\) through terminal 1 of a switch \(S\). After the capacitor has become fully charged, the switch is thrown at time \(t = 0\) to terminal 2, disconnecting the battery and connecting the capacitor directly across an ideal inductor of inductance \(L\). What are the peak current in the resulting circuit and the first elapsed time \(t > 0\) at which this peak current occurs?

![A circuit schematic drawn in thin black lines on a white background. On the left, a vertical branch contains a DC voltage source labeled \(\mathcal{E}\), represented by a longer thin horizontal line above a shorter thicker horizontal line. A top horizontal wire extends rightward to a single-pole double-throw switch labeled \(S\). The switch has a movable arm hinged at a node above a central vertical branch containing a capacitor labeled \(C\), represented by two identical parallel horizontal plates separated by a gap. Terminal 1 of the switch connects to the left wire leading to the voltage source. Terminal 2 of the switch connects to a top horizontal wire continuing rightward to a vertical branch containing an inductor labeled \(L\), drawn as four consecutive rounded loops. A single continuous bottom horizontal wire connects the bottom of the voltage source, the bottom of the capacitor, and the bottom of the inductor to complete both loops. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604817-pV3PNe.jpg)

- **A.** Peak current: \(\mathcal{E}\sqrt{\dfrac{C}{L}}\) Elapsed time: \(\pi\sqrt{LC}\)
- **B.** Peak current: \(\mathcal{E}\sqrt{\dfrac{C}{L}}\) Elapsed time: \(\dfrac{\pi}{2}\sqrt{LC}\)
- **C.** Peak current: \(\mathcal{E}\sqrt{\dfrac{C}{2L}}\) Elapsed time: \(\dfrac{\pi}{2}\sqrt{LC}\)
- **D.** Peak current: \(\mathcal{E}\sqrt{\dfrac{C}{2L}}\) Elapsed time: \(\pi\sqrt{LC}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125044/*