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title: "An ideal battery of electromotive force \\(\\mathcal{E}\\) is connected to a bridge network of five resistors as shown. The upper-left resistor has resistance \\(R_1 = R\\), the lower-left resistor has resistance \\(R_3 = 2R\\), the upper-right resistor has resistance \\(R_2 = 2R\\), and the lower-right resistor has resistance \\(R_4 = R\\). A central resistor with resistance \\(R_5 = R\\) connects junction C (between \\(R_1\\) and \\(R_2\\)) to junction D (between \\(R_3\\) and \\(R_4\\)). What is the electric potential at junction C relative to the grounded negative terminal of the battery, and what is the direction of the electric current through resistor \\(R_5\\)?"
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url: "https://nerd-notes.com/ubq/118479/"
date_modified: "2026-08-04T08:10:44+00:00"
---

# An ideal battery of electromotive force \(\mathcal{E}\) is connected to a bridge network of five resistors as shown. The upper-left resistor has resistance \(R_1 = R\), the lower-left resistor has resistance \(R_3 = 2R\), the upper-right resistor has resistance \(R_2 = 2R\), and the lower-right resistor has resistance \(R_4 = R\). A central resistor with resistance \(R_5 = R\) connects junction C (between \(R_1\) and \(R_2\)) to junction D (between \(R_3\) and \(R_4\)). What is the electric potential at junction C relative to the grounded negative terminal of the battery, and what is the direction of the electric current through resistor \(R_5\)?

An ideal battery of electromotive force \(\mathcal{E}\) is connected to a bridge network of five resistors as shown. The upper-left resistor has resistance \(R_1 = R\), the lower-left resistor has resistance \(R_3 = 2R\), the upper-right resistor has resistance \(R_2 = 2R\), and the lower-right resistor has resistance \(R_4 = R\). A central resistor with resistance \(R_5 = R\) connects junction C (between \(R_1\) and \(R_2\)) to junction D (between \(R_3\) and \(R_4\)). What is the electric potential at junction C relative to the grounded negative terminal of the battery, and what is the direction of the electric current through resistor \(R_5\)?

![A schematic diagram of a DC circuit containing a DC power source and five resistors. On the left side, a vertical branch contains an ideal battery labeled \mathcal{E}, with its long positive terminal bar at the top and short negative terminal bar at the bottom, accompanied by a ground symbol at the bottom wire. The top wire extends horizontally to the right to node A, and the bottom wire extends horizontally to the right to node B. From node A, two parallel paths split: an upper path goes through resistor R_1 to node C, and a lower path goes through resistor R_3 to node D. From node C, resistor R_2 continues horizontally to node B. From node D, resistor R_4 continues horizontally to node B. A vertical branch connects node C and node D, containing resistor R_5. Labels R_1 = R, R_2 = 2R, R_3 = 2R, R_4 = R, and R_5 = R are placed adjacent to their respective resistors. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831044-hwMuDX.jpg)

- **A.** Potential \(V_C = \dfrac{4}{7}\mathcal{E}\); Current direction: From C to D
- **B.** Potential \(V_C = \dfrac{4}{7}\mathcal{E}\); Current direction: From D to C
- **C.** Potential \(V_C = \dfrac{2}{3}\mathcal{E}\); Current direction: From C to D
- **D.** Potential \(V_C = \dfrac{2}{3}\mathcal{E}\); Current direction: From D to C

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118479/*