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?