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title: "A circuit contains an ideal battery of potential difference \\(\\Delta V\\), a series resistor of resistance \\(R_0\\), and two parallel branches with resistances \\(R_1 = R\\) and \\(R_2 = 2R\\). A switch \\(S\\) is connected in series with resistor \\(R_2\\) and is initially closed. If switch \\(S\\) is opened, which of the following correctly describes the change in the electric current \\(I_1\\) through resistor \\(R_1\\) and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/120410/"
date_modified: "2026-08-23T04:34:30+00:00"
---

# A circuit contains an ideal battery of potential difference \(\Delta V\), a series resistor of resistance \(R_0\), and two parallel branches with resistances \(R_1 = R\) and \(R_2 = 2R\). A switch \(S\) is connected in series with resistor \(R_2\) and is initially closed. If switch \(S\) is opened, which of the following correctly describes the change in the electric current \(I_1\) through resistor \(R_1\) and provides the correct justification?

A circuit contains an ideal battery of potential difference \(\Delta V\), a series resistor of resistance \(R_0\), and two parallel branches with resistances \(R_1 = R\) and \(R_2 = 2R\). A switch \(S\) is connected in series with resistor \(R_2\) and is initially closed. If switch \(S\) is opened, which of the following correctly describes the change in the electric current \(I_1\) through resistor \(R_1\) and provides the correct justification?

![A rectangular schematic circuit diagram. On the left vertical segment is a DC voltage source labeled \(\Delta V\), with a longer horizontal line on top and a shorter parallel line below. From the positive terminal, the wire extends to the right along the top rail through a zigzag resistor labeled R_0 to a top junction dot. The circuit splits into two parallel vertical branches: the left branch contains a zigzag resistor labeled R_1 = R; the right branch contains an open-knife switch symbol labeled S in series with a zigzag resistor labeled R_2 = 2R. Both vertical branches reconnect at a bottom junction dot, which connects along the bottom rail 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-1-1787459669-J421AP.jpg)

- **A.** The current \(I_1\) decreases because the equivalent resistance of the circuit increases, which decreases the total current supplied by the battery and reduces the current entering the parallel combination.
- **B.** The current \(I_1\) remains the same because the resistance \(R_1\) and the total potential difference \(\Delta V\) supplied by the battery remain unchanged.
- **C.** The current \(I_1\) increases because the total current entering the junction is conserved and the current that previously flowed through resistor \(R_2\) is entirely redirected through resistor \(R_1\).
- **D.** The current \(I_1\) increases because the equivalent resistance of the circuit increases, decreasing the potential difference across \(R_0\) and increasing the potential difference across \(R_1\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120410/*