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title: "A bridge circuit is connected to an ideal battery of electromotive force \\(\\mathcal{E} = 12\\text{ V}\\), as shown in the diagram. Resistors \\(R_1 = 2.0\\text{ }\\Omega\\) and \\(R_2 = 6.0\\text{ }\\Omega\\) form the left branch, while resistors \\(R_3 = 6.0\\text{ }\\Omega\\) and \\(R_4 = 2.0\\text{ }\\Omega\\) form the right branch. A central resistor \\(R_5 = 3.0\\text{ }\\Omega\\) connects node \\(a\\) between \\(R_1\\) and \\(R_2\\) to node \\(b\\) between \\(R_3\\) and \\(R_4\\). What is the magnitude of the electric current flowing through resistor \\(R_5\\)?"
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url: "https://nerd-notes.com/ubq/121601/"
date_modified: "2026-08-23T05:24:18+00:00"
---

# A bridge circuit is connected to an ideal battery of electromotive force \(\mathcal{E} = 12\text{ V}\), as shown in the diagram. Resistors \(R_1 = 2.0\text{ }\Omega\) and \(R_2 = 6.0\text{ }\Omega\) form the left branch, while resistors \(R_3 = 6.0\text{ }\Omega\) and \(R_4 = 2.0\text{ }\Omega\) form the right branch. A central resistor \(R_5 = 3.0\text{ }\Omega\) connects node \(a\) between \(R_1\) and \(R_2\) to node \(b\) between \(R_3\) and \(R_4\). What is the magnitude of the electric current flowing through resistor \(R_5\)?

A bridge circuit is connected to an ideal battery of electromotive force \(\mathcal{E} = 12\text{ V}\), as shown in the diagram. Resistors \(R_1 = 2.0\text{ }\Omega\) and \(R_2 = 6.0\text{ }\Omega\) form the left branch, while resistors \(R_3 = 6.0\text{ }\Omega\) and \(R_4 = 2.0\text{ }\Omega\) form the right branch. A central resistor \(R_5 = 3.0\text{ }\Omega\) connects node \(a\) between \(R_1\) and \(R_2\) to node \(b\) between \(R_3\) and \(R_4\). What is the magnitude of the electric current flowing through resistor \(R_5\)?

![A circuit schematic drawn with solid black lines on a white background. At the top, a horizontal wire connects to the positive terminal of an ideal DC voltage source labeled \(\mathcal{E} = 12\text{ V}\), while the bottom horizontal wire connects to the negative terminal. Two parallel vertical branches extend between the top and bottom wires. The left branch contains resistor \(R_1 = 2.0\text{ }\Omega\) on its upper half and resistor \(R_2 = 6.0\text{ }\Omega\) on its lower half, with a labeled junction dot \(a\) between them. The right branch contains resistor \(R_3 = 6.0\text{ }\Omega\) on its upper half and resistor \(R_4 = 2.0\text{ }\Omega\) on its lower half, with a labeled junction dot \(b\) between them. A horizontal branch containing a resistor labeled \(R_5 = 3.0\text{ }\Omega\) connects junction \(a\) to junction \(b\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462658-KcRnCP.jpg)

- **A.** \(0.50\text{ A}\)
- **B.** \(0.75\text{ A}\)
- **C.** \(1.0\text{ A}\)
- **D.** \(2.0\text{ A}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121601/*