---
title: "A circuit consists of an ideal battery of electromotive force \\(\\mathcal{E}\\), a resistor of resistance \\(R\\), an inductor of inductance \\(L\\), and an open switch, all connected in series. At time \\(t = 0\\), the switch is closed. At what time \\(t\\) is the rate at which energy is stored in the magnetic field of the inductor equal to the rate at which energy is dissipated as thermal energy in the resistor?"
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url: "https://nerd-notes.com/ubq/118653/"
date_modified: "2026-08-04T08:13:30+00:00"
---

# A circuit consists of an ideal battery of electromotive force \(\mathcal{E}\), a resistor of resistance \(R\), an inductor of inductance \(L\), and an open switch, all connected in series. At time \(t = 0\), the switch is closed. At what time \(t\) is the rate at which energy is stored in the magnetic field of the inductor equal to the rate at which energy is dissipated as thermal energy in the resistor?

A circuit consists of an ideal battery of electromotive force \(\mathcal{E}\), a resistor of resistance \(R\), an inductor of inductance \(L\), and an open switch, all connected in series. At time \(t = 0\), the switch is closed. At what time \(t\) is the rate at which energy is stored in the magnetic field of the inductor equal to the rate at which energy is dissipated as thermal energy in the resistor?

![A single-loop circuit schematic drawn with black lines on a white background. On the left vertical segment, a battery labeled \(\mathcal{E}\) with long top bar and short bottom bar. On the top horizontal segment, an open switch labeled S. On the right vertical segment, a resistor drawn as a zig-zag line labeled R. On the bottom horizontal segment, an inductor drawn as a series of four semi-circular loops labeled L. No other labels, text, or elements appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831210-MeCyiU.jpg)

- **A.** \(\dfrac{L}{2R} \ln 2\)
- **B.** \(\dfrac{L}{R} \ln 2\)
- **C.** \(\dfrac{2L}{R} \ln 2\)
- **D.** \(\dfrac{L}{R} \ln 3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118653/*