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title: "A planar resistor network consists of two concentric circular loops: an inner loop with nodes \\(A\\), \\(B\\), \\(C\\), and \\(D\\), and an outer loop with nodes \\(A’\\), \\(B’\\), \\(C’\\), and \\(D’\\). Each of the four circular arc segments on the inner loop, each of the four circular arc segments on the outer loop, and each of the four radial spokes connecting corresponding nodes (\\(AA’\\), \\(BB’\\), \\(CC’\\), and \\(DD’\\)) consists of an identical resistor of resistance \\(R\\). An ideal battery maintaining potential difference \\(V_0\\) is connected across nodes \\(A\\) and \\(C\\) on the inner loop, setting node potential \\(V_A = V_0\\) and grounding node \\(C\\) such that \\(V_C = 0\\). Which of the following expressions represents the electric potential \\(V_{A’}\\) at node \\(A’\\) on the outer loop?"
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url: "https://nerd-notes.com/ubq/116127/"
date_modified: "2026-08-03T10:15:14+00:00"
---

# A planar resistor network consists of two concentric circular loops: an inner loop with nodes \(A\), \(B\), \(C\), and \(D\), and an outer loop with nodes \(A’\), \(B’\), \(C’\), and \(D’\). Each of the four circular arc segments on the inner loop, each of the four circular arc segments on the outer loop, and each of the four radial spokes connecting corresponding nodes (\(AA’\), \(BB’\), \(CC’\), and \(DD’\)) consists of an identical resistor of resistance \(R\). An ideal battery maintaining potential difference \(V_0\) is connected across nodes \(A\) and \(C\) on the inner loop, setting node potential \(V_A = V_0\) and grounding node \(C\) such that \(V_C = 0\). Which of the following expressions represents the electric potential \(V_{A’}\) at node \(A’\) on the outer loop?

A planar resistor network consists of two concentric circular loops: an inner loop with nodes \(A\), \(B\), \(C\), and \(D\), and an outer loop with nodes \(A'\), \(B'\), \(C'\), and \(D'\). Each of the four circular arc segments on the inner loop, each of the four circular arc segments on the outer loop, and each of the four radial spokes connecting corresponding nodes (\(AA'\), \(BB'\), \(CC'\), and \(DD'\)) consists of an identical resistor of resistance \(R\). An ideal battery maintaining potential difference \(V_0\) is connected across nodes \(A\) and \(C\) on the inner loop, setting node potential \(V_A = V_0\) and grounding node \(C\) such that \(V_C = 0\). Which of the following expressions represents the electric potential \(V_{A'}\) at node \(A'\) on the outer loop?

![A schematic diagram of a planar concentric circuit network. Two concentric circles represent an inner loop and an outer loop. The inner circle features four nodes labeled A at the top, B at the right, C at the bottom, and D at the left. The outer circle features four corresponding nodes labeled A' at the top, B' at the right, C' at the bottom, and D' at the left. Each of the four circular arcs between adjacent nodes on the inner loop contains a resistor symbol labeled R. Each of the four circular arcs between adjacent nodes on the outer loop contains a resistor symbol labeled R. Four straight radial segments connect A to A', B to B', C to C', and D to D', each containing a resistor symbol labeled R. An ideal battery labeled V_0 is connected between node A and node C, with a ground symbol attached to node C. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785752113-t8DS1w.jpg)

- **A.** \( \dfrac{2}{3} V_0 \)
- **B.** \( \dfrac{1}{2} V_0 \)
- **C.** \( \dfrac{3}{4} V_0 \)
- **D.** \( \dfrac{1}{3} V_0 \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116127/*