---
title: "A circuit consists of an ideal battery of constant emf \\(\\varepsilon\\), a resistor of resistance \\(R\\), an inductor of inductance \\(L\\), and an open switch connected in series. At time \\(t = 0\\), the switch is closed. At the instant when the current in the circuit reaches half of its maximum steady-state value, what fraction of the total energy delivered by the battery up to that time is stored in the magnetic field of the inductor?"
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url: "https://nerd-notes.com/ubq/118752/"
date_modified: "2026-08-04T08:14:08+00:00"
---

# A circuit consists of an ideal battery of constant emf \(\varepsilon\), a resistor of resistance \(R\), an inductor of inductance \(L\), and an open switch connected in series. At time \(t = 0\), the switch is closed. At the instant when the current in the circuit reaches half of its maximum steady-state value, what fraction of the total energy delivered by the battery up to that time is stored in the magnetic field of the inductor?

A circuit consists of an ideal battery of constant emf \(\varepsilon\), a resistor of resistance \(R\), an inductor of inductance \(L\), and an open switch connected in series. At time \(t = 0\), the switch is closed. At the instant when the current in the circuit reaches half of its maximum steady-state value, what fraction of the total energy delivered by the battery up to that time is stored in the magnetic field of the inductor?

![A rectangular schematic diagram of a single-loop circuit. On the left vertical branch is an ideal DC battery labeled \varepsilon, with its long positive terminal bar at the top and short negative terminal bar at the bottom. On the top horizontal branch is an open switch labeled S. On the right vertical branch is a resistor labeled R, drawn as a zig-zag line. On the bottom horizontal branch is an inductor labeled L, drawn as a series of four semicircular loops. Straight thin lines connect all components into a closed loop except at the open switch. No other labels or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831248-Wg1Ll7.jpg)

- **A.** \(\dfrac{1}{4\ln 2}\)
- **B.** \(\dfrac{1}{4(2\ln 2 + 1)}\)
- **C.** \(\dfrac{1}{2(2\ln 2 - 1)}\)
- **D.** \(\dfrac{1}{4(2\ln 2 - 1)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118752/*