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title: "An ideal circuit consists of an inductor of inductance \\(L\\) connected in a closed loop with a capacitor of capacitance \\(C\\). At time \\(t = 0\\), the capacitor holds an initial charge \\(Q_0\\) and the current in the circuit is zero. The circuit is analyzed for progressively smaller values of inductance while the initial charge \\(Q_0\\) and capacitance \\(C\\) are held constant. In the limit as \\(L \\to 0^+\\), what happens to the maximum discharge rate of the capacitor, \\(\\left|\\dfrac{dq}{dt}\\right|_{\\max}\\), and the maximum energy stored in the magnetic field of the inductor, \\(U_{L,\\max}\\)?"
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url: "https://nerd-notes.com/ubq/125018/"
date_modified: "2026-09-28T14:13:17+00:00"
---

# An ideal circuit consists of an inductor of inductance \(L\) connected in a closed loop with a capacitor of capacitance \(C\). At time \(t = 0\), the capacitor holds an initial charge \(Q_0\) and the current in the circuit is zero. The circuit is analyzed for progressively smaller values of inductance while the initial charge \(Q_0\) and capacitance \(C\) are held constant. In the limit as \(L \to 0^+\), what happens to the maximum discharge rate of the capacitor, \(\left|\dfrac{dq}{dt}\right|_{\max}\), and the maximum energy stored in the magnetic field of the inductor, \(U_{L,\max}\)?

An ideal circuit consists of an inductor of inductance \(L\) connected in a closed loop with a capacitor of capacitance \(C\). At time \(t = 0\), the capacitor holds an initial charge \(Q_0\) and the current in the circuit is zero. The circuit is analyzed for progressively smaller values of inductance while the initial charge \(Q_0\) and capacitance \(C\) are held constant. In the limit as \(L \to 0^+\), what happens to the maximum discharge rate of the capacitor, \(\left|\dfrac{dq}{dt}\right|_{\max}\), and the maximum energy stored in the magnetic field of the inductor, \(U_{L,\max}\)?

![A single rectangular circuit loop oriented horizontally. The left vertical branch contains a parallel-plate capacitor represented by two equal-length parallel horizontal lines separated by a narrow gap, with a label \(C\) positioned to the left of the gap. The top plate is marked with a plus sign and the bottom plate with a minus sign. The right vertical branch contains an inductor drawn as four adjacent semicircular loops curved toward the right, with a label \(L\) positioned to the right of the coils. The top and bottom horizontal branches consist of solid straight lines connecting the capacitor and inductor to form a single closed conductive loop. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604797-SiIBVG.jpg)

- **A.** \(\left|\dfrac{dq}{dt}\right|_{\max}\) approaches a finite non-zero value, and \(U_{L,\max}\) approaches zero.
- **B.** \(\left|\dfrac{dq}{dt}\right|_{\max}\) approaches a finite non-zero value, and \(U_{L,\max}\) remains equal to \(\dfrac{Q_0^2}{2C}\).
- **C.** \(\left|\dfrac{dq}{dt}\right|_{\max}\) approaches infinity, and \(U_{L,\max}\) approaches infinity.
- **D.** \(\left|\dfrac{dq}{dt}\right|_{\max}\) approaches infinity, and \(U_{L,\max}\) remains equal to \(\dfrac{Q_0^2}{2C}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125018/*