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title: "In the bridge circuit shown, an ideal battery of potential difference \\(V_0\\) is connected across junctions \\(A\\) and \\(D\\). The upper branch consists of two resistors, \\(R_1 = R\\) and \\(R_2 = 3R\\), connected at node \\(B\\). The lower branch consists of two resistors, \\(R_3 = 2R\\) and \\(R_4 = 2R\\), connected at node \\(C\\). A central resistor of resistance \\(R_0 = R\\) connects node \\(B\\) to node \\(C\\). What is the direction of the electric current through the central resistor \\(R_0\\), and what is the magnitude of this current?"
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url: "https://nerd-notes.com/ubq/118465/"
date_modified: "2026-08-04T08:10:21+00:00"
---

# In the bridge circuit shown, an ideal battery of potential difference \(V_0\) is connected across junctions \(A\) and \(D\). The upper branch consists of two resistors, \(R_1 = R\) and \(R_2 = 3R\), connected at node \(B\). The lower branch consists of two resistors, \(R_3 = 2R\) and \(R_4 = 2R\), connected at node \(C\). A central resistor of resistance \(R_0 = R\) connects node \(B\) to node \(C\). What is the direction of the electric current through the central resistor \(R_0\), and what is the magnitude of this current?

In the bridge circuit shown, an ideal battery of potential difference \(V_0\) is connected across junctions \(A\) and \(D\). The upper branch consists of two resistors, \(R_1 = R\) and \(R_2 = 3R\), connected at node \(B\). The lower branch consists of two resistors, \(R_3 = 2R\) and \(R_4 = 2R\), connected at node \(C\). A central resistor of resistance \(R_0 = R\) connects node \(B\) to node \(C\). What is the direction of the electric current through the central resistor \(R_0\), and what is the magnitude of this current?

![A schematic of a bridge circuit connected to an ideal battery of voltage V_0. Node A is on the left, connected to the positive terminal of the battery. Node D is on the right, connected to the negative terminal of the battery. The top branch goes from A through resistor R_1 = R to node B, then through resistor R_2 = 3R to node D. The bottom branch goes from A through resistor R_3 = 2R to node C, then through resistor R_4 = 2R to node D. A central resistor labeled R_0 = R connects node B to node C. No other labels, lines, text, or elements appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831021-kgl4Nh.jpg)

- **A.** Direction: From \(B\) to \(C\) Magnitude: \(\dfrac{V_0}{11R}\)
- **B.** Direction: From \(B\) to \(C\) Magnitude: \(\dfrac{V_0}{4R}\)
- **C.** Direction: From \(C\) to \(B\) Magnitude: \(\dfrac{V_0}{11R}\)
- **D.** Direction: From \(C\) to \(B\) Magnitude: \(\dfrac{V_0}{4R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118465/*