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title: "A circuit contains an ideal battery of potential difference \\(\\Delta V\\), an open switch \\(S\\), and two parallel branches. Branch 1 contains a resistor of resistance \\(R\\). Branch 2 contains a resistor of resistance \\(R\\) connected in series with an initially uncharged capacitor of capacitance \\(C\\). Switch \\(S\\) is closed at time \\(t = 0\\). Which of the following claims and justifications correctly describes the current in Branch 2 a long time after the switch is closed?"
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url: "https://nerd-notes.com/ubq/117162/"
date_modified: "2026-08-04T06:44:51+00:00"
---

# A circuit contains an ideal battery of potential difference \(\Delta V\), an open switch \(S\), and two parallel branches. Branch 1 contains a resistor of resistance \(R\). Branch 2 contains a resistor of resistance \(R\) connected in series with an initially uncharged capacitor of capacitance \(C\). Switch \(S\) is closed at time \(t = 0\). Which of the following claims and justifications correctly describes the current in Branch 2 a long time after the switch is closed?

A circuit contains an ideal battery of potential difference \(\Delta V\), an open switch \(S\), and two parallel branches. Branch 1 contains a resistor of resistance \(R\). Branch 2 contains a resistor of resistance \(R\) connected in series with an initially uncharged capacitor of capacitance \(C\). Switch \(S\) is closed at time \(t = 0\). Which of the following claims and justifications correctly describes the current in Branch 2 a long time after the switch is closed?

![A schematic diagram showing a DC circuit. On the left side, a vertical battery labeled Delta V with a switch S in series on the top wire. The wire splits into two parallel vertical branches to the right. The middle branch labeled Branch 1 contains a single resistor R. The rightmost branch labeled Branch 2 contains a resistor R in series with a parallel-plate capacitor C. No other components, labels, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1785825890-CjYB0J.jpg)

- **A.** The current in Branch 2 is \(\dfrac{\Delta V}{R}\) because the capacitor acts as a wire with zero resistance when fully charged.
- **B.** The current in Branch 2 is \(\dfrac{\Delta V}{2R}\) because the fully charged capacitor acts as an additional resistor of resistance \(R\).
- **C.** The current in Branch 2 is zero because the potential difference across the capacitor equals \(\Delta V\), preventing further net flow of charge into that branch.
- **D.** The current in Branch 2 is zero because the capacitor has become completely discharged over time, leaving no charge available to flow.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117162/*