---
title: "An ideal LC circuit consists of an inductor of inductance L and a capacitor of capacitance C.  Initially, the capacitor holds a maximum charge Q_max and the current in the circuit is zero.  The circuit oscillates freely, and at a subsequent instant during the first quarter-cycle, the charge on the capacitor is q = (1/2)Q_max.  Which of the following correctly ranks the fractional electric energy U_E / U_tot, the fractional magnetic energy U_B / U_tot, the fractional current I / I_max, and the fractional rate of energy transfer P / P_max at this instant, where P = |dU_E / dt| and P_max is the maximum possible rate of energy transfer in the circuit?"
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url: "https://nerd-notes.com/ubq/125040/"
date_modified: "2026-09-28T14:13:32+00:00"
---

# An ideal LC circuit consists of an inductor of inductance L and a capacitor of capacitance C.

Initially, the capacitor holds a maximum charge Q_max and the current in the circuit is zero.

The circuit oscillates freely, and at a subsequent instant during the first quarter-cycle, the charge on the capacitor is q = (1/2)Q_max.

Which of the following correctly ranks the fractional electric energy U_E / U_tot, the fractional magnetic energy U_B / U_tot, the fractional current I / I_max, and the fractional rate of energy transfer P / P_max at this instant, where P = |dU_E / dt| and P_max is the maximum possible rate of energy transfer in the circuit?

An ideal LC circuit consists of an inductor of inductance L and a capacitor of capacitance C.

Initially, the capacitor holds a maximum charge Q_max and the current in the circuit is zero.

The circuit oscillates freely, and at a subsequent instant during the first quarter-cycle, the charge on the capacitor is q = (1/2)Q_max.

Which of the following correctly ranks the fractional electric energy U_E / U_tot, the fractional magnetic energy U_B / U_tot, the fractional current I / I_max, and the fractional rate of energy transfer P / P_max at this instant, where P = |dU_E / dt| and P_max is the maximum possible rate of energy transfer in the circuit?

![A single rectangular circuit loop oriented with horizontal top and bottom branches and vertical left and right branches. The top horizontal wire contains a parallel-plate capacitor represented by two equal vertical parallel segments separated by a small gap, with the label C directly above the gap. The right vertical wire contains an inductor represented by four semicircular loops forming a coil, with the label L directly to the right of the coil. The bottom and left segments are continuous solid straight lines representing ideal connecting wires. No arrows, meters, switches, or other components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604812-24HiNy.jpg)

- **A.** \(\dfrac{U_E}{U_{\text{tot}}} = \dfrac{U_B}{U_{\text{tot}}} < \dfrac{I}{I_{\max}} = \dfrac{P}{P_{\max}}\)
- **B.** \(\dfrac{U_E}{U_{\text{tot}}} < \dfrac{U_B}{U_{\text{tot}}} < \dfrac{I}{I_{\max}} < \dfrac{P}{P_{\max}}\)
- **C.** \(\dfrac{U_E}{U_{\text{tot}}} < \dfrac{P}{P_{\max}} < \dfrac{U_B}{U_{\text{tot}}} < \dfrac{I}{I_{\max}}\)
- **D.** \(\dfrac{U_E}{U_{\text{tot}}} < \dfrac{U_B}{U_{\text{tot}}} < \dfrac{I}{I_{\max}} = \dfrac{P}{P_{\max}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125040/*