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title: "A five-resistor bridge network is connected between terminals \\(X\\) and \\(Y\\). The upper branch consists of two resistors of resistance \\(R_1 = 6.0\\text{ }\\Omega\\) and \\(R_2 = 12.0\\text{ }\\Omega\\) in series. The lower branch consists of two resistors of resistance \\(R_3 = 3.0\\text{ }\\Omega\\) and \\(R_4 = 6.0\\text{ }\\Omega\\) in series. A bridging resistor of resistance \\(R_5 = 10.0\\text{ }\\Omega\\) connects the node between \\(R_1\\) and \\(R_2\\) to the node between \\(R_3\\) and \\(R_4\\). What is the equivalent resistance between terminals \\(X\\) and \\(Y\\)?"
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url: "https://nerd-notes.com/ubq/121559/"
date_modified: "2026-08-23T05:24:01+00:00"
---

# A five-resistor bridge network is connected between terminals \(X\) and \(Y\). The upper branch consists of two resistors of resistance \(R_1 = 6.0\text{ }\Omega\) and \(R_2 = 12.0\text{ }\Omega\) in series. The lower branch consists of two resistors of resistance \(R_3 = 3.0\text{ }\Omega\) and \(R_4 = 6.0\text{ }\Omega\) in series. A bridging resistor of resistance \(R_5 = 10.0\text{ }\Omega\) connects the node between \(R_1\) and \(R_2\) to the node between \(R_3\) and \(R_4\). What is the equivalent resistance between terminals \(X\) and \(Y\)?

A five-resistor bridge network is connected between terminals \(X\) and \(Y\). The upper branch consists of two resistors of resistance \(R_1 = 6.0\text{ }\Omega\) and \(R_2 = 12.0\text{ }\Omega\) in series. The lower branch consists of two resistors of resistance \(R_3 = 3.0\text{ }\Omega\) and \(R_4 = 6.0\text{ }\Omega\) in series. A bridging resistor of resistance \(R_5 = 10.0\text{ }\Omega\) connects the node between \(R_1\) and \(R_2\) to the node between \(R_3\) and \(R_4\). What is the equivalent resistance between terminals \(X\) and \(Y\)?

![A schematic diagram showing a bridge circuit between terminals X on the far left and Y on the far right. From terminal X, the path splits into two parallel branches. The top branch goes through resistor R_1 to node A, and then from node A through resistor R_2 to terminal Y. The bottom branch goes through resistor R_3 to node B, and then from node B through resistor R_4 to terminal Y. A vertical branch containing resistor R_5 connects node A directly to node B. Resistor labels are R_1 = 6.0 \Omega, R_2 = 12.0 \Omega, R_3 = 3.0 \Omega, R_4 = 6.0 \Omega, and R_5 = 10.0 \Omega. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1787462641-G3QIY4.jpg)

- **A.** \(2.0\text{ }\Omega\)
- **B.** \(3.8\text{ }\Omega\)
- **C.** \(4.5\text{ }\Omega\)
- **D.** \(6.0\text{ }\Omega\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121559/*