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title: "A circuit junction connects four branches, as shown in the diagram. Currents in three of the branches are given as functions of time \\(t\\) for \\(t \\ge 0\\):  – Branch 1: \\(I_1(t) = (3.0 \\text{ A/s})t\\) directed into the junction – Branch 2: \\(I_2(t) = 4.0 \\text{ A}\\) directed into the junction – Branch 3: \\(I_3(t) = (1.0 \\text{ A/s})t + 1.0 \\text{ A}\\) directed away from the junction  The fourth branch connects the junction to an initially uncharged capacitor. At time \\(t = 2.0 \\text{ s}\\), what is the instantaneous net current entering the capacitor, and what is the total charge that has accumulated on the capacitor between \\(t = 0\\) and \\(t = 2.0 \\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/118393/"
date_modified: "2026-08-04T08:09:53+00:00"
---

# A circuit junction connects four branches, as shown in the diagram. Currents in three of the branches are given as functions of time \(t\) for \(t \ge 0\):

– Branch 1: \(I_1(t) = (3.0 \text{ A/s})t\) directed into the junction
– Branch 2: \(I_2(t) = 4.0 \text{ A}\) directed into the junction
– Branch 3: \(I_3(t) = (1.0 \text{ A/s})t + 1.0 \text{ A}\) directed away from the junction

The fourth branch connects the junction to an initially uncharged capacitor. At time \(t = 2.0 \text{ s}\), what is the instantaneous net current entering the capacitor, and what is the total charge that has accumulated on the capacitor between \(t = 0\) and \(t = 2.0 \text{ s}\)?

A circuit junction connects four branches, as shown in the diagram. Currents in three of the branches are given as functions of time \(t\) for \(t \ge 0\):

- Branch 1: \(I_1(t) = (3.0 \text{ A/s})t\) directed into the junction
- Branch 2: \(I_2(t) = 4.0 \text{ A}\) directed into the junction
- Branch 3: \(I_3(t) = (1.0 \text{ A/s})t + 1.0 \text{ A}\) directed away from the junction

The fourth branch connects the junction to an initially uncharged capacitor. At time \(t = 2.0 \text{ s}\), what is the instantaneous net current entering the capacitor, and what is the total charge that has accumulated on the capacitor between \(t = 0\) and \(t = 2.0 \text{ s}\)?

![A circuit schematic centered on a single circular junction dot labeled J. Four straight wire segments meet at junction J. A horizontal wire on the left extends to junction J, featuring a rightward-pointing arrow labeled I_1(t). A vertical wire extending from above meets junction J, featuring a downward-pointing arrow labeled I_2(t). A horizontal wire on the right extends away from junction J, featuring a rightward-pointing arrow labeled I_3(t). A vertical wire extends downward from junction J to the top plate of a parallel-plate capacitor, which consists of two parallel horizontal line segments. An arrow pointing downward along this wire indicates net current entering the capacitor. The top plate is labeled P, and the bottom plate is connected to a standard three-line ground symbol. No other labels, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830993-5GvwfZ.jpg)

- **A.** Net current: \(5.0 \text{ A}\); Accumulated charge: \(10.0 \text{ C}\)
- **B.** Net current: \(7.0 \text{ A}\); Accumulated charge: \(14.0 \text{ C}\)
- **C.** Net current: \(7.0 \text{ A}\); Accumulated charge: \(10.0 \text{ C}\)
- **D.** Net current: \(13.0 \text{ A}\); Accumulated charge: \(18.0 \text{ C}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118393/*