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title: "In the circuit shown, an ideal battery of EMF \\(\\mathcal{E}\\) is connected in series with an open switch \\(S\\) to a bridge network. One parallel branch consists of a resistor of resistance \\(R\\) connected in series with a resistor of resistance \\(2R\\) at node \\(X\\). The other parallel branch consists of a resistor of resistance \\(2R\\) connected in series with a resistor of resistance \\(R\\) at node \\(Y\\). An unenergized inductor of inductance \\(L\\) connects node \\(X\\) to node \\(Y\\). The switch is closed at time \\(t = 0\\). Which of the following correctly describes the effective behavior of the inductor and the magnitude of the current through it immediately after the switch is closed (\\(t = 0^+\\)) and long after the switch is closed (\\(t \\to \\infty\\))?"
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url: "https://nerd-notes.com/ubq/125022/"
date_modified: "2026-09-28T14:13:19+00:00"
---

# In the circuit shown, an ideal battery of EMF \(\mathcal{E}\) is connected in series with an open switch \(S\) to a bridge network. One parallel branch consists of a resistor of resistance \(R\) connected in series with a resistor of resistance \(2R\) at node \(X\). The other parallel branch consists of a resistor of resistance \(2R\) connected in series with a resistor of resistance \(R\) at node \(Y\). An unenergized inductor of inductance \(L\) connects node \(X\) to node \(Y\). The switch is closed at time \(t = 0\). Which of the following correctly describes the effective behavior of the inductor and the magnitude of the current through it immediately after the switch is closed (\(t = 0^+\)) and long after the switch is closed (\(t \to \infty\))?

In the circuit shown, an ideal battery of EMF \(\mathcal{E}\) is connected in series with an open switch \(S\) to a bridge network. One parallel branch consists of a resistor of resistance \(R\) connected in series with a resistor of resistance \(2R\) at node \(X\). The other parallel branch consists of a resistor of resistance \(2R\) connected in series with a resistor of resistance \(R\) at node \(Y\). An unenergized inductor of inductance \(L\) connects node \(X\) to node \(Y\). The switch is closed at time \(t = 0\). Which of the following correctly describes the effective behavior of the inductor and the magnitude of the current through it immediately after the switch is closed (\(t = 0^+\)) and long after the switch is closed (\(t \to \infty\))?

![A rectangular circuit schematic in grayscale. On the left vertical wire, an ideal battery is oriented vertically with the long positive plate on top and short negative plate on bottom, labeled \(\mathcal{E}\). An open switch labeled \(S\) is on the top horizontal wire leading from the battery. To the right, the top wire meets a junction that splits into two vertical parallel paths. The left path contains a zig-zag resistor labeled \(R\) above node \(X\), and a zig-zag resistor labeled \(2R\) below node \(X\). The right path contains a zig-zag resistor labeled \(2R\) above node \(Y\), and a zig-zag resistor labeled \(R\) below node \(Y\). A horizontal branch connects node \(X\) and node \(Y\), containing an inductor symbol with four rounded loops labeled \(L\). Both vertical paths recombine at a bottom junction that connects back along the bottom horizontal wire to the negative terminal of the battery. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604798-wqlT15.jpg)

- **A.** At \(t = 0^+\), it behaves as a short circuit with current \(\dfrac{\mathcal{E}}{4R}\); as \(t \to \infty\), it behaves as an open circuit with current \(0\).
- **B.** At \(t = 0^+\), it behaves as an open circuit with current \(0\); as \(t \to \infty\), it behaves as a short circuit with current \(\dfrac{\mathcal{E}}{4R}\).
- **C.** At \(t = 0^+\), it behaves as an open circuit with current \(0\); as \(t \to \infty\), it behaves as a short circuit with current \(\dfrac{\mathcal{E}}{2R}\).
- **D.** At \(t = 0^+\), it behaves as an open circuit with current \(0\); as \(t \to \infty\), it behaves as a short circuit with current \(\dfrac{3\mathcal{E}}{4R}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125022/*