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title: "An ideal LC circuit consists of an inductor of inductance L and an air-filled parallel-plate capacitor of plate separation d and plate area A, oscillating with maximum charge Q_{\\text{max}} and angular frequency \\omega. The electrical system is modeled by an analogous mechanical system consisting of a block of mass m oscillating on a frictionless horizontal surface connected to an ideal spring of force constant k. If the plate separation d of the capacitor is doubled while Q_{\\text{max}} and L remain constant, which of the following correctly describes the resulting change in the circuit’s angular frequency \\omega, the change in the maximum magnetic energy U_{B,\\text{max}} stored in the inductor, and the analogous modification to the spring constant k in the mechanical oscillator?"
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url: "https://nerd-notes.com/ubq/125059/"
date_modified: "2026-09-28T14:14:08+00:00"
---

# An ideal LC circuit consists of an inductor of inductance L and an air-filled parallel-plate capacitor of plate separation d and plate area A, oscillating with maximum charge Q_{\text{max}} and angular frequency \omega. The electrical system is modeled by an analogous mechanical system consisting of a block of mass m oscillating on a frictionless horizontal surface connected to an ideal spring of force constant k. If the plate separation d of the capacitor is doubled while Q_{\text{max}} and L remain constant, which of the following correctly describes the resulting change in the circuit’s angular frequency \omega, the change in the maximum magnetic energy U_{B,\text{max}} stored in the inductor, and the analogous modification to the spring constant k in the mechanical oscillator?

An ideal LC circuit consists of an inductor of inductance L and an air-filled parallel-plate capacitor of plate separation d and plate area A, oscillating with maximum charge Q_{\text{max}} and angular frequency \omega. The electrical system is modeled by an analogous mechanical system consisting of a block of mass m oscillating on a frictionless horizontal surface connected to an ideal spring of force constant k. If the plate separation d of the capacitor is doubled while Q_{\text{max}} and L remain constant, which of the following correctly describes the resulting change in the circuit's angular frequency \omega, the change in the maximum magnetic energy U_{B,\text{max}} stored in the inductor, and the analogous modification to the spring constant k in the mechanical oscillator?

- **A.** | \(\omega\): Increases | \(U_{B,\text{max}}\): Increases | Analogous \(k\): Doubles |
- **B.** | \(\omega\): Increases | \(U_{B,\text{max}}\): Decreases | Analogous \(k\): Halves |
- **C.** | \(\omega\): Decreases | \(U_{B,\text{max}}\): Increases | Analogous \(k\): Halves |
- **D.** | \(\omega\): Decreases | \(U_{B,\text{max}}\): Decreases | Analogous \(k\): Doubles |

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125059/*