A cylindrical metal wire of resistivity \(\rho\), initial length \(L_0\), and uniform cross-sectional area \(A_0\) has an initial electrical resistance \(R_0\). The wire is drawn out uniformly to a new length \(L_1\) such that its total volume remains constant. The stretched wire is then cut into \(N\) identical segments of equal length, and all \(N\) segments are connected in parallel to form a single resistor network. Which of the following expressions correctly represents the equivalent resistance \(R_p\) of this parallel combination in terms of \(R_0\), \(L_0\), \(L_1\), and \(N\)?