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title: "Six identical resistors, each having resistance \\(R\\), are connected end-to-end to form a closed regular hexagonal loop with vertices labeled \\(A\\) through \\(F\\). An ideal direct-current power source is connected across two adjacent vertices, \\(A\\) and \\(B\\), establishing a current entering vertex \\(A\\) and exiting vertex \\(B\\). Which of the following statements correctly identifies the equivalent resistance \\(R_{eq}\\) between vertices \\(A\\) and \\(B\\) and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/121566/"
date_modified: "2026-08-23T05:24:03+00:00"
---

# Six identical resistors, each having resistance \(R\), are connected end-to-end to form a closed regular hexagonal loop with vertices labeled \(A\) through \(F\). An ideal direct-current power source is connected across two adjacent vertices, \(A\) and \(B\), establishing a current entering vertex \(A\) and exiting vertex \(B\). Which of the following statements correctly identifies the equivalent resistance \(R_{eq}\) between vertices \(A\) and \(B\) and provides the correct physical justification?

Six identical resistors, each having resistance \(R\), are connected end-to-end to form a closed regular hexagonal loop with vertices labeled \(A\) through \(F\). An ideal direct-current power source is connected across two adjacent vertices, \(A\) and \(B\), establishing a current entering vertex \(A\) and exiting vertex \(B\). Which of the following statements correctly identifies the equivalent resistance \(R_{eq}\) between vertices \(A\) and \(B\) and provides the correct physical justification?

![A regular hexagon circuit schematic in grayscale. The bottom horizontal side contains a zigzag resistor symbol between vertex \(A\) at the bottom-left and vertex \(B\) at the bottom-right. The remaining five sides each contain an identical zigzag resistor symbol, connecting consecutively through vertices \(C\) (middle-right), \(D\) (top-right), \(E\) (top-left), and \(F\) (middle-left) back to \(A\). Each of the six resistors is labeled with the symbol \(R\). Small solid dots mark each vertex \(A, B, C, D, E, F\). Two lead wires extend downward from vertex \(A\) and vertex \(B\) to open terminal circles. No other lines, labels, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462642-3GmUYV.jpg)

- **A.** The equivalent resistance is \(\dfrac{5}{6}R\) because the single-resistor path between \(A\) and \(B\) is in parallel with the remaining five series resistors, resulting in \(\dfrac{5}{6}\) of the total current flowing through the single resistor.
- **B.** The equivalent resistance is \(\dfrac{6}{5}R\) because summing the reciprocal resistances of the single-resistor branch and the five-resistor series branch yields the direct ratio of branch lengths.
- **C.** The equivalent resistance is \(\dfrac{1}{2}R\) because the geometric symmetry of the regular hexagon forces the total current to divide equally between the clockwise and counterclockwise paths.
- **D.** The equivalent resistance is \(\dfrac{1}{6}R\) because all six identical resistors are connected in a parallel configuration between the two terminals.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121566/*