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title: "In the circuit shown, an ideal battery of electromotive force \\(\\mathcal{E}\\) is connected in series with a switch \\(S\\) across two parallel branches: Branch 1 contains an ideal inductor of inductance \\(L\\) in series with a resistor of resistance \\(R_1\\), and Branch 2 contains a resistor of resistance \\(R_2\\). The switch has been closed for a time \\(t \\gg \\dfrac{L}{R_1}\\), establishing a steady-state current. At time \\(t = 0\\), switch \\(S\\) is opened to disconnect the battery. In the limit as \\(t \\to 0^+\\), which of the following correctly describes the current through resistor \\(R_2\\) and the magnitude of the potential difference \\(|V_L|\\) across the inductor?"
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url: "https://nerd-notes.com/ubq/125028/"
date_modified: "2026-09-28T14:13:23+00:00"
---

# In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with a switch \(S\) across two parallel branches: Branch 1 contains an ideal inductor of inductance \(L\) in series with a resistor of resistance \(R_1\), and Branch 2 contains a resistor of resistance \(R_2\). The switch has been closed for a time \(t \gg \dfrac{L}{R_1}\), establishing a steady-state current. At time \(t = 0\), switch \(S\) is opened to disconnect the battery. In the limit as \(t \to 0^+\), which of the following correctly describes the current through resistor \(R_2\) and the magnitude of the potential difference \(|V_L|\) across the inductor?

In the circuit shown, an ideal battery of electromotive force \(\mathcal{E}\) is connected in series with a switch \(S\) across two parallel branches: Branch 1 contains an ideal inductor of inductance \(L\) in series with a resistor of resistance \(R_1\), and Branch 2 contains a resistor of resistance \(R_2\). The switch has been closed for a time \(t \gg \dfrac{L}{R_1}\), establishing a steady-state current. At time \(t = 0\), switch \(S\) is opened to disconnect the battery. In the limit as \(t \to 0^+\), which of the following correctly describes the current through resistor \(R_2\) and the magnitude of the potential difference \(|V_L|\) across the inductor?

![A rectangular circuit schematic composed of three vertical parallel branches connected by horizontal top and bottom wires. The leftmost vertical branch contains an open-circle switch labeled S near the top and a DC voltage source labeled \mathcal{E} below it, with the longer horizontal plate on top. The middle vertical branch contains an ideal inductor symbol with four consecutive rounded loops labeled L at the top, in series with a zig-zag resistor symbol labeled R_1 below it. The rightmost vertical branch contains a zig-zag resistor symbol labeled R_2. Solid horizontal line segments connect the top ends of all three branches together, and solid horizontal line segments connect the bottom ends of all three branches together. All circuit wiring is represented by thin solid lines. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1790604803-E1zFJh.jpg)

- **A.** The current through resistor \(R_2\) is directed downward with magnitude \(\dfrac{\mathcal{E}}{R_2}\), and the potential difference across the inductor has magnitude \(0\).
- **B.** The current through resistor \(R_2\) is directed upward with magnitude \(\dfrac{\mathcal{E}}{R_1}\), and the potential difference across the inductor has magnitude \(\mathcal{E}\left(1 + \dfrac{R_2}{R_1}\right)\).
- **C.** The current through resistor \(R_2\) is directed upward with magnitude \(\dfrac{\mathcal{E}}{R_2}\), and the potential difference across the inductor has magnitude \(\mathcal{E}\).
- **D.** The current through resistor \(R_2\) is directed upward with magnitude \(\dfrac{\mathcal{E}}{R_1 + R_2}\), and the potential difference across the inductor has magnitude \(\mathcal{E}\dfrac{R_2}{R_1}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125028/*