---
title: "An ideal battery of electromotive force \\(\\mathcal{E}\\) and a switch \\(S\\) are connected in parallel with two branches, as shown in the circuit diagram. One branch contains a resistor of resistance \\(2R\\), and the other branch contains an ideal inductor of inductance \\(L\\) connected in series with a resistor of resistance \\(R\\). The switch has been closed for a long time until steady-state conditions are reached, and is then opened at time \\(t = 0\\). Which of the following correctly ranks the magnitudes of the potential differences across the inductor \\((\\Delta V_L)\\), the resistor of resistance \\(R\\) \\((\\Delta V_R)\\), and the resistor of resistance \\(2R\\) \\((\\Delta V_{2R})\\) immediately after the switch is opened at \\(t = 0^+\\)?"
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url: "https://nerd-notes.com/ubq/121313/"
date_modified: "2026-08-23T04:59:40+00:00"
---

# An ideal battery of electromotive force \(\mathcal{E}\) and a switch \(S\) are connected in parallel with two branches, as shown in the circuit diagram. One branch contains a resistor of resistance \(2R\), and the other branch contains an ideal inductor of inductance \(L\) connected in series with a resistor of resistance \(R\). The switch has been closed for a long time until steady-state conditions are reached, and is then opened at time \(t = 0\). Which of the following correctly ranks the magnitudes of the potential differences across the inductor \((\Delta V_L)\), the resistor of resistance \(R\) \((\Delta V_R)\), and the resistor of resistance \(2R\) \((\Delta V_{2R})\) immediately after the switch is opened at \(t = 0^+\)?

An ideal battery of electromotive force \(\mathcal{E}\) and a switch \(S\) are connected in parallel with two branches, as shown in the circuit diagram. One branch contains a resistor of resistance \(2R\), and the other branch contains an ideal inductor of inductance \(L\) connected in series with a resistor of resistance \(R\). The switch has been closed for a long time until steady-state conditions are reached, and is then opened at time \(t = 0\). Which of the following correctly ranks the magnitudes of the potential differences across the inductor \((\Delta V_L)\), the resistor of resistance \(R\) \((\Delta V_R)\), and the resistor of resistance \(2R\) \((\Delta V_{2R})\) immediately after the switch is opened at \(t = 0^+\)?

![A schematic circuit diagram with three vertical parallel branches connected across top and bottom horizontal conducting rails. The leftmost branch contains an ideal DC battery labeled \(\mathcal{E}\) with its longer positive line at the top, in series with a switch labeled \(S\) located directly above the battery. The middle branch contains a resistor labeled \(2R\). The rightmost branch contains an inductor coil labeled \(L\) positioned directly above a resistor labeled \(R\). No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1787461180-FVSYHA.jpg)

- **A.** \(\Delta V_L > \Delta V_{2R} > \Delta V_R\)
- **B.** \(\Delta V_{2R} > \Delta V_L = \Delta V_R\)
- **C.** \(\Delta V_{2R} > \Delta V_R > \Delta V_L\)
- **D.** \(\Delta V_L > \Delta V_R > \Delta V_{2R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121313/*