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title: "A circuit contains an ideal battery of potential difference \\(V_0\\), an open switch \\(S\\), three identical resistors each of resistance \\(R\\) (labeled \\(R_1\\), \\(R_2\\), and \\(R_3\\)), and an ideal inductor of inductance \\(L\\), as shown in the schematic. The branch currents are labeled \\(I_1\\), \\(I_2\\), and \\(I_3\\). Switch \\(S\\) is closed at time \\(t = 0\\). Which of the following correctly ranks the magnitudes of the currents immediately after the switch is closed?"
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url: "https://nerd-notes.com/ubq/118742/"
date_modified: "2026-08-04T08:14:04+00:00"
---

# A circuit contains an ideal battery of potential difference \(V_0\), an open switch \(S\), three identical resistors each of resistance \(R\) (labeled \(R_1\), \(R_2\), and \(R_3\)), and an ideal inductor of inductance \(L\), as shown in the schematic. The branch currents are labeled \(I_1\), \(I_2\), and \(I_3\). Switch \(S\) is closed at time \(t = 0\). Which of the following correctly ranks the magnitudes of the currents immediately after the switch is closed?

A circuit contains an ideal battery of potential difference \(V_0\), an open switch \(S\), three identical resistors each of resistance \(R\) (labeled \(R_1\), \(R_2\), and \(R_3\)), and an ideal inductor of inductance \(L\), as shown in the schematic. The branch currents are labeled \(I_1\), \(I_2\), and \(I_3\). Switch \(S\) is closed at time \(t = 0\). Which of the following correctly ranks the magnitudes of the currents immediately after the switch is closed?

![A schematic circuit diagram consisting of a main loop that splits into two parallel branches. On the far left, a vertical wire contains an ideal DC battery labeled V_0 with its positive terminal on top, in series with an open switch labeled S above the battery. The top horizontal wire extends to the right and contains a resistor labeled R_1. To the right of R_1, the circuit splits into two parallel horizontal branches: the upper parallel branch contains a resistor labeled R_2, and the lower parallel branch contains an ideal inductor labeled L in series with a resistor labeled R_3. The two parallel branches recombine on the right and connect to the bottom horizontal wire returning to the negative terminal of the battery. An arrow labeled I_1 points to the right through resistor R_1. An arrow labeled I_2 points to the right through resistor R_2. An arrow labeled I_3 points to the right through the branch containing L and R_3. No other components or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831244-semBOj.jpg)

- **A.** \(I_1 > I_2 > I_3 > 0\)
- **B.** \(I_1 = I_2 > I_3\)
- **C.** \(I_1 > I_2 = I_3 > 0\)
- **D.** \(I_3 > I_1 = I_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118742/*