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title: "An ideal battery of potential difference \\(V_0\\) is connected in series with an open switch \\(S\\) and a resistor \\(R_1 = R\\). This combination is connected across a parallel network consisting of two branches: Branch 1 contains a resistor \\(R_2 = 2R\\) in series with an initially uncharged capacitor \\(C\\), and Branch 2 contains a resistor \\(R_3 = 2R\\). At time \\(t = 0\\), switch \\(S\\) is closed. Which row in the table correctly identifies the initial current \\(I_3(0^+)\\) through resistor \\(R_3\\) immediately after the switch is closed, and describes the behavior of current \\(I_3(t)\\) for \\(t > 0\\)?  | Row | Initial Current \\(I_3(0^+)\\) | Behavior of \\(I_3(t)\\) for \\(t > 0\\) | | :— | :— | :— | | Row A | \\(\\dfrac{V_0}{2R}\\) | Exponentially decreases toward zero | | Row B | \\(\\dfrac{V_0}{4R}\\) | Exponentially decreases toward zero | | Row C | \\(\\dfrac{V_0}{4R}\\) | Exponentially increases toward \\(\\dfrac{V_0}{3R}\\) | | Row D | \\(\\dfrac{V_0}{3R}\\) | Exponentially decreases toward \\(\\dfrac{V_0}{4R}\\) |"
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url: "https://nerd-notes.com/ubq/118439/"
date_modified: "2026-08-04T08:10:04+00:00"
---

# An ideal battery of potential difference \(V_0\) is connected in series with an open switch \(S\) and a resistor \(R_1 = R\). This combination is connected across a parallel network consisting of two branches: Branch 1 contains a resistor \(R_2 = 2R\) in series with an initially uncharged capacitor \(C\), and Branch 2 contains a resistor \(R_3 = 2R\). At time \(t = 0\), switch \(S\) is closed. Which row in the table correctly identifies the initial current \(I_3(0^+)\) through resistor \(R_3\) immediately after the switch is closed, and describes the behavior of current \(I_3(t)\) for \(t > 0\)?

| Row | Initial Current \(I_3(0^+)\) | Behavior of \(I_3(t)\) for \(t > 0\) |
| :— | :— | :— |
| Row A | \(\dfrac{V_0}{2R}\) | Exponentially decreases toward zero |
| Row B | \(\dfrac{V_0}{4R}\) | Exponentially decreases toward zero |
| Row C | \(\dfrac{V_0}{4R}\) | Exponentially increases toward \(\dfrac{V_0}{3R}\) |
| Row D | \(\dfrac{V_0}{3R}\) | Exponentially decreases toward \(\dfrac{V_0}{4R}\) |

An ideal battery of potential difference \(V_0\) is connected in series with an open switch \(S\) and a resistor \(R_1 = R\). This combination is connected across a parallel network consisting of two branches: Branch 1 contains a resistor \(R_2 = 2R\) in series with an initially uncharged capacitor \(C\), and Branch 2 contains a resistor \(R_3 = 2R\). At time \(t = 0\), switch \(S\) is closed. Which row in the table correctly identifies the initial current \(I_3(0^+)\) through resistor \(R_3\) immediately after the switch is closed, and describes the behavior of current \(I_3(t)\) for \(t > 0\)?

| Row | Initial Current \(I_3(0^+)\) | Behavior of \(I_3(t)\) for \(t > 0\) |
| :--- | :--- | :--- |
| Row A | \(\dfrac{V_0}{2R}\) | Exponentially decreases toward zero |
| Row B | \(\dfrac{V_0}{4R}\) | Exponentially decreases toward zero |
| Row C | \(\dfrac{V_0}{4R}\) | Exponentially increases toward \(\dfrac{V_0}{3R}\) |
| Row D | \(\dfrac{V_0}{3R}\) | Exponentially decreases toward \(\dfrac{V_0}{4R}\) |

![A schematic diagram of a DC circuit. At the top left, an ideal battery labeled V_0 is oriented vertically with its positive terminal on top. Connected to the positive terminal, a top horizontal wire extends to the right, containing an open switch labeled S, followed by a resistor labeled R_1 = R. The wire reaches a top junction node. From this node, two parallel vertical branches descend to a bottom junction node. The left branch contains a resistor labeled R_2 = 2R in series above an uncharged capacitor labeled C. The right branch contains a resistor labeled R_3 = 2R. A single bottom horizontal wire connects the bottom junction node back 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-1-1785831004-JAUvNW.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118439/*