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title: "In the circuit shown, an ideal battery with potential difference \\(V_0\\) is connected to three resistors (\\(R_1 = R\\), \\(R_2 = 2R\\), \\(R_3 = R\\)), an ideal inductor \\(L\\), and a switch \\(S\\). The switch \\(S\\) has been closed for a long time. At time \\(t = 0\\), switch \\(S\\) is opened. Which of the following expressions represents the magnitude of the current \\(I(t)\\) through resistor \\(R_2\\) as a function of time \\(t\\) for \\(t \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/118754/"
date_modified: "2026-08-04T08:14:08+00:00"
---

# In the circuit shown, an ideal battery with potential difference \(V_0\) is connected to three resistors (\(R_1 = R\), \(R_2 = 2R\), \(R_3 = R\)), an ideal inductor \(L\), and a switch \(S\). The switch \(S\) has been closed for a long time. At time \(t = 0\), switch \(S\) is opened. Which of the following expressions represents the magnitude of the current \(I(t)\) through resistor \(R_2\) as a function of time \(t\) for \(t \ge 0\)?

In the circuit shown, an ideal battery with potential difference \(V_0\) is connected to three resistors (\(R_1 = R\), \(R_2 = 2R\), \(R_3 = R\)), an ideal inductor \(L\), and a switch \(S\). The switch \(S\) has been closed for a long time. At time \(t = 0\), switch \(S\) is opened. Which of the following expressions represents the magnitude of the current \(I(t)\) through resistor \(R_2\) as a function of time \(t\) for \(t \ge 0\)?

![A schematic diagram of an electric circuit drawn with straight black lines forming two adjacent rectangular loops. On the far left vertical wire of the left loop is a DC battery labeled \(V_0\) with its longer positive terminal on top. On the top horizontal wire of the left loop is a switch labeled \(S\) shown in an open position and a resistor labeled \(R_1 = R\) in series. A shared vertical wire separates the left and right loops, containing a resistor labeled \(R_2 = 2R\). On the far right vertical wire of the right loop, a resistor labeled \(R_3 = R\) is connected in series above an inductor coil labeled \(L\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831248-owvOHW.jpg)

- **A.** \(\dfrac{V_0}{5R} e^{-3Rt/L}\)
- **B.** \(\dfrac{2V_0}{5R} e^{-Rt/L}\)
- **C.** \(\dfrac{2V_0}{5R} e^{-3Rt/L}\)
- **D.** \(\dfrac{3V_0}{5R} e^{-3Rt/L}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118754/*