Three wires each of length L, cross-sectional area A and resistivity ρ are connected as shown in the figure (one wire from X to Y directly, and two wires in parallel from X to Y, then one wire from Y to Z). These are to be replaced by another wire of same resistivity such that the resistance between points X and Z does not change. If L₁ is the length and A₁ is the cross-sectional area of the new wire, then which one among the following is correct?

Each wire has resistance R = ρL/A. Between X and Y there are two wires in parallel, giving resistance R/2 = ρL/(2A). From Y to Z there is one wire of resistance R = ρL/A. Total resistance from X to Z = R/2 + R = 3R/2 = 3ρL/(2A). For a single replacement wire of length L₁ and area A₁: R' = ρL₁/A₁ = 3ρL/(2A), giving L₁/A₁ = 3L/(2A). Among the choices, L₁ = 2L and A₁ = 3A satisfies this: 2L/3A = (2/3)(L/A), while we need (3/2)(L/A). Re-examining: option (c) gives L₁/A₁ = 2L/3A, but we need 3L/2A. Hmm. Let me redo: option (a) gives 3L/2A ✓. So L₁ = 3L and A₁ = 2A is correct. Correcting: the right answer is (a).