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title: "An ideal battery of potential difference \\(\\varepsilon\\) is connected to a network of four identical resistors, each of resistance \\(R\\). Resistor \\(R_1\\) connects the positive terminal of the battery to node \\(B\\), and resistor \\(R_2\\) is connected between node \\(B\\) and the grounded negative terminal. Resistor \\(R_3\\) connects node \\(B\\) to node \\(C\\), and resistor \\(R_4\\) connects node \\(C\\) to the grounded negative terminal. What is the electric potential \\(V_B\\) at node \\(B\\) relative to the grounded negative terminal?"
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url: "https://nerd-notes.com/ubq/116108/"
date_modified: "2026-08-03T10:15:05+00:00"
---

# An ideal battery of potential difference \(\varepsilon\) is connected to a network of four identical resistors, each of resistance \(R\). Resistor \(R_1\) connects the positive terminal of the battery to node \(B\), and resistor \(R_2\) is connected between node \(B\) and the grounded negative terminal. Resistor \(R_3\) connects node \(B\) to node \(C\), and resistor \(R_4\) connects node \(C\) to the grounded negative terminal. What is the electric potential \(V_B\) at node \(B\) relative to the grounded negative terminal?

An ideal battery of potential difference \(\varepsilon\) is connected to a network of four identical resistors, each of resistance \(R\). Resistor \(R_1\) connects the positive terminal of the battery to node \(B\), and resistor \(R_2\) is connected between node \(B\) and the grounded negative terminal. Resistor \(R_3\) connects node \(B\) to node \(C\), and resistor \(R_4\) connects node \(C\) to the grounded negative terminal. What is the electric potential \(V_B\) at node \(B\) relative to the grounded negative terminal?

![A rectangular circuit diagram featuring an ideal DC battery on the left vertical wire, oriented with its positive terminal at the top labeled \(\varepsilon\). The bottom wire is horizontal, continuous, and grounded at the bottom-left corner. From the top of the battery, a horizontal wire extends rightward through a resistor symbol labeled \(R_1\) to a junction dot labeled \(B\). From junction \(B\), a vertical wire goes down through a resistor symbol labeled \(R_2\) to the bottom wire. From junction \(B\), a horizontal wire extends rightward through a resistor symbol labeled \(R_3\) to a junction dot labeled \(C\). From junction \(C\), a vertical wire goes down through a resistor symbol labeled \(R_4\) to the bottom wire. All four resistors have identical zig-zag symbols. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785752105-lAF1ph.jpg)

- **A.** \(\dfrac{1}{5}\varepsilon\)
- **B.** \(\dfrac{2}{5}\varepsilon\)
- **C.** \(\dfrac{1}{2}\varepsilon\)
- **D.** \(\dfrac{3}{5}\varepsilon\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116108/*