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title: "An RL circuit consists of an ideal switch, a resistor of resistance \\(R\\), an inductor of inductance \\(L\\), and an ideal battery of constant emf \\(\\varepsilon\\), all connected in series. At time \\(t = 0\\), the switch is closed. In terms of the circuit’s time constant \\(\\tau = \\dfrac{L}{R}\\), at what time \\(t\\) does the energy stored in the magnetic field of the inductor reach half of its maximum steady-state value?"
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url: "https://nerd-notes.com/ubq/118698/"
date_modified: "2026-08-04T08:13:48+00:00"
---

# An RL circuit consists of an ideal switch, a resistor of resistance \(R\), an inductor of inductance \(L\), and an ideal battery of constant emf \(\varepsilon\), all connected in series. At time \(t = 0\), the switch is closed. In terms of the circuit’s time constant \(\tau = \dfrac{L}{R}\), at what time \(t\) does the energy stored in the magnetic field of the inductor reach half of its maximum steady-state value?

An RL circuit consists of an ideal switch, a resistor of resistance \(R\), an inductor of inductance \(L\), and an ideal battery of constant emf \(\varepsilon\), all connected in series. At time \(t = 0\), the switch is closed. In terms of the circuit's time constant \(\tau = \dfrac{L}{R}\), at what time \(t\) does the energy stored in the magnetic field of the inductor reach half of its maximum steady-state value?

![A schematic diagram of a single-loop circuit containing a DC voltage source labeled \(\varepsilon\) on the left branch, a open switch on the top horizontal wire, a resistor labeled \(R\) on the right branch, and an inductor labeled \(L\) on the right branch connected in series with the resistor. The circuit forms a closed rectangular loop.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831227-Eo2SV1.jpg)

- **A.** \(\tau \ln(2)\)
- **B.** \(\tau \ln\left(\dfrac{\sqrt{2}}{\sqrt{2}-1}\right)\)
- **C.** \(\tau \ln\left(\sqrt{2}\right)\)
- **D.** \(\tau \ln\left(1 + \sqrt{2}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118698/*