---
title: "A circuit consists of an ideal inductor of inductance \\(L\\) and an ideal capacitor of capacitance \\(C\\) connected in series with a time-varying voltage source that provides an electromotive force \\(\\mathcal{E}(t) = \\mathcal{E}_0 \\cos(\\omega t)\\). The charge on the capacitor oscillates according to \\(q(t) = Q_{\\text{max}} \\cos(\\omega t)\\), where \\(Q_{\\text{max}}\\)"
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url: "https://nerd-notes.com/ubq/118736/"
date_modified: "2026-08-04T08:14:02+00:00"
---

# A circuit consists of an ideal inductor of inductance \(L\) and an ideal capacitor of capacitance \(C\) connected in series with a time-varying voltage source that provides an electromotive force \(\mathcal{E}(t) = \mathcal{E}_0 \cos(\omega t)\). The charge on the capacitor oscillates according to \(q(t) = Q_{\text{max}} \cos(\omega t)\), where \(Q_{\text{max}}\)

A circuit consists of an ideal inductor of inductance \(L\) and an ideal capacitor of capacitance \(C\) connected in series with a time-varying voltage source that provides an electromotive force \(\mathcal{E}(t) = \mathcal{E}_0 \cos(\omega t)\). The charge on the capacitor oscillates according to \(q(t) = Q_{\text{max}} \cos(\omega t)\), where \(Q_{\text{max}}\)

![A single-loop schematic diagram containing three components connected in series: a sinusoidal AC voltage source on the left labeled \mathcal{E}(t) = \mathcal{E}_0 \cos(\omega t), an inductor on the top branch labeled L, and a parallel-plate capacitor on the right branch labeled C. Wires complete a closed rectangular circuit loop. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1785831241-75QpAh.jpg)

- **A.** \(\dfrac{\mathcal{E}_0 C}{1 + \omega^2 LC}\)
- **B.** \(\dfrac{\mathcal{E}_0 C}{1 - \omega \sqrt{LC}}\)
- **C.** \(\dfrac{\mathcal{E}_0 C}{1 - \omega^2 LC}\)
- **D.** \(\dfrac{\mathcal{E}_0 C}{\omega^2 LC}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118736/*