---
title: "In the circuit shown, an ideal battery of EMF \\(\\mathcal{E}\\) is connected in series with a two-position switch \\(S\\), a resistor of resistance \\(R_1\\), and an ideal inductor of inductance \\(L\\). The switch has been closed in position 1 for a long time so that the circuit has reached a steady state. At time \\(t = 0\\), the switch is instantaneously moved to position 2, disconnecting the battery and connecting the inductor directly across a second resistor of resistance \\(R_2\\) in an isolated closed loop. Which of the following expressions represents the magnitude of the potential difference \\(V(t)\\) across the resistor of resistance \\(R_2\\) as a function of time \\(t\\) for \\(t > 0\\)?"
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url: "https://nerd-notes.com/ubq/121331/"
date_modified: "2026-08-23T04:59:45+00:00"
---

# In the circuit shown, an ideal battery of EMF \(\mathcal{E}\) is connected in series with a two-position switch \(S\), a resistor of resistance \(R_1\), and an ideal inductor of inductance \(L\). The switch has been closed in position 1 for a long time so that the circuit has reached a steady state. At time \(t = 0\), the switch is instantaneously moved to position 2, disconnecting the battery and connecting the inductor directly across a second resistor of resistance \(R_2\) in an isolated closed loop. Which of the following expressions represents the magnitude of the potential difference \(V(t)\) across the resistor of resistance \(R_2\) as a function of time \(t\) for \(t > 0\)?

In the circuit shown, an ideal battery of EMF \(\mathcal{E}\) is connected in series with a two-position switch \(S\), a resistor of resistance \(R_1\), and an ideal inductor of inductance \(L\). The switch has been closed in position 1 for a long time so that the circuit has reached a steady state. At time \(t = 0\), the switch is instantaneously moved to position 2, disconnecting the battery and connecting the inductor directly across a second resistor of resistance \(R_2\) in an isolated closed loop. Which of the following expressions represents the magnitude of the potential difference \(V(t)\) across the resistor of resistance \(R_2\) as a function of time \(t\) for \(t > 0\)?

![A circuit schematic showing a two-position single-pole double-throw switch S. The center common terminal of switch S connects to the top of a vertical inductor labeled L. On the left, switch terminal 1 connects to a series branch containing an ideal battery labeled \(\mathcal{E}\) with its positive terminal upward and a resistor labeled R_1. On the right, switch terminal 2 connects to a vertical branch containing a resistor labeled R_2. The bottoms of the battery branch, the inductor branch, and the R_2 branch all meet at a common horizontal bottom wire. A dashed arrow near switch S indicates moving the switch arm from contact 1 to contact 2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461185-vzOJOn.jpg)

- **A.** \(V(t) = \mathcal{E} e^{-\frac{R_2 t}{L}}\)
- **B.** \(V(t) = \mathcal{E}\left(\dfrac{R_1}{R_2}\right) e^{-\frac{R_2 t}{L}}\)
- **C.** \(V(t) = \mathcal{E}\left(\dfrac{R_2}{R_1}\right) e^{-\frac{R_1 t}{L}}\)
- **D.** \(V(t) = \mathcal{E}\left(\dfrac{R_2}{R_1}\right) e^{-\frac{R_2 t}{L}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121331/*