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title: "A circuit consists of an ideal battery of emf \\(\\mathcal{E}\\), an open switch \\(S\\), an ideal inductor of inductance \\(L\\), and a resistor of resistance \\(R\\), all connected in series. At time \\(t = 0\\), switch \\(S\\) is closed. Consider the following four quantities:  – \\(P_1\\): The rate at which energy is delivered by the battery immediately after the switch is closed (\\(t = 0^+\\)) – \\(P_2\\): The rate at which energy is stored in the magnetic field of the inductor when the current is \\(I = \\dfrac{\\mathcal{E}}{2R}\\) – \\(P_3\\): The rate at which energy is dissipated in the resistor when the current is \\(I = \\dfrac{\\mathcal{E}}{2R}\\) – \\(P_4\\): The rate at which energy is delivered by the battery long after the switch is closed (\\(t \\to \\infty\\))  Which of the following correctly ranks these four power values?"
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url: "https://nerd-notes.com/ubq/118738/"
date_modified: "2026-08-04T08:14:03+00:00"
---

# A circuit consists of an ideal battery of emf \(\mathcal{E}\), an open switch \(S\), an ideal inductor of inductance \(L\), and a resistor of resistance \(R\), all connected in series. At time \(t = 0\), switch \(S\) is closed. Consider the following four quantities:

– \(P_1\): The rate at which energy is delivered by the battery immediately after the switch is closed (\(t = 0^+\))
– \(P_2\): The rate at which energy is stored in the magnetic field of the inductor when the current is \(I = \dfrac{\mathcal{E}}{2R}\)
– \(P_3\): The rate at which energy is dissipated in the resistor when the current is \(I = \dfrac{\mathcal{E}}{2R}\)
– \(P_4\): The rate at which energy is delivered by the battery long after the switch is closed (\(t \to \infty\))

Which of the following correctly ranks these four power values?

A circuit consists of an ideal battery of emf \(\mathcal{E}\), an open switch \(S\), an ideal inductor of inductance \(L\), and a resistor of resistance \(R\), all connected in series. At time \(t = 0\), switch \(S\) is closed. Consider the following four quantities:

- \(P_1\): The rate at which energy is delivered by the battery immediately after the switch is closed (\(t = 0^+\))
- \(P_2\): The rate at which energy is stored in the magnetic field of the inductor when the current is \(I = \dfrac{\mathcal{E}}{2R}\)
- \(P_3\): The rate at which energy is dissipated in the resistor when the current is \(I = \dfrac{\mathcal{E}}{2R}\)
- \(P_4\): The rate at which energy is delivered by the battery long after the switch is closed (\(t \to \infty\))

Which of the following correctly ranks these four power values?

![A rectangular single-loop circuit diagram drawn with clean black lines on a white background. On the left vertical wire, an ideal DC voltage source is oriented vertically, labeled \mathcal{E}, with a long parallel horizontal bar on top representing the positive terminal and a shorter bar on the bottom representing the negative terminal. On the top horizontal wire, a single-pole single-throw switch labeled S is shown in an open position tilted upward at approximately 30 degrees. On the right vertical wire, an inductor labeled L is drawn as a series of four connected semicircular loops, followed in series on the same vertical wire by a resistor labeled R drawn as a zigzag line with four peaks. Arrows indicating current direction are absent. No other components, text, or background grids appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831242-MtSsox.jpg)

- **A.** \(P_1 < P_3 < P_2 < P_4\)
- **B.** \(P_1 = P_2 < P_3 < P_4\)
- **C.** \(P_1 < P_2 < P_3 < P_4\)
- **D.** \(P_1 < P_2 = P_3 < P_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118738/*