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title: "An ideal battery of electromotive force \\(\\mathcal{E} = 24 \\text{ V}\\) is connected in series with a resistor \\(R_1 = 4.0 \\text{ }\\Omega\\), and this combination is connected across two parallel branches. The first branch contains a switch \\(S_1\\) in series with a resistor \\(R_2 = 8.0 \\text{ }\\Omega\\), and the second branch contains a switch \\(S_2\\) in series with a resistor \\(R_3 = 8.0 \\text{ }\\Omega\\). Initially, switch \\(S_1\\) is closed and switch \\(S_2\\) is open. Switch \\(S_2\\) is then also closed. What is the total electric current supplied by the battery after switch \\(S_2\\) is closed?"
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url: "https://nerd-notes.com/ubq/118380/"
date_modified: "2026-08-04T08:09:48+00:00"
---

# An ideal battery of electromotive force \(\mathcal{E} = 24 \text{ V}\) is connected in series with a resistor \(R_1 = 4.0 \text{ }\Omega\), and this combination is connected across two parallel branches. The first branch contains a switch \(S_1\) in series with a resistor \(R_2 = 8.0 \text{ }\Omega\), and the second branch contains a switch \(S_2\) in series with a resistor \(R_3 = 8.0 \text{ }\Omega\). Initially, switch \(S_1\) is closed and switch \(S_2\) is open. Switch \(S_2\) is then also closed. What is the total electric current supplied by the battery after switch \(S_2\) is closed?

An ideal battery of electromotive force \(\mathcal{E} = 24 \text{ V}\) is connected in series with a resistor \(R_1 = 4.0 \text{ }\Omega\), and this combination is connected across two parallel branches. The first branch contains a switch \(S_1\) in series with a resistor \(R_2 = 8.0 \text{ }\Omega\), and the second branch contains a switch \(S_2\) in series with a resistor \(R_3 = 8.0 \text{ }\Omega\). Initially, switch \(S_1\) is closed and switch \(S_2\) is open. Switch \(S_2\) is then also closed. What is the total electric current supplied by the battery after switch \(S_2\) is closed?

![A rectangular DC circuit schematic. The left vertical wire contains an ideal battery labeled \(\mathcal{E}\), with its long positive terminal line on top and short negative terminal line on the bottom. The top horizontal wire contains a resistor labeled \(R_1 = 4.0\text{ }\Omega\). To the right, the circuit divides into two parallel vertical branches. The inner vertical branch contains a single-pole switch labeled \(S_1\) in series with a resistor labeled \(R_2 = 8.0\text{ }\Omega\). The outer vertical branch contains a single-pole switch labeled \(S_2\) in series with a resistor labeled \(R_3 = 8.0\text{ }\Omega\). The bottom wire connects all three vertical branches back to the negative terminal of the battery. No other components, text, or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830987-E4mFhk.jpg)

- **A.** \(2.0 \text{ A}\)
- **B.** \(3.0 \text{ A}\)
- **C.** \(4.0 \text{ A}\)
- **D.** \(6.0 \text{ A}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118380/*