Four resistors R₁ = 12 , , R₂ = 2 , , R₃ = 4 , , and R₄ = 12 , are connected in series between five successive nodes numbered 1, 2, 3, 4, and 5 in that order. An ideal conducting wire connects node 1 to node 4, and another ideal conducting wire connects node 2 to node 5. The equivalent resistance between node 1 and node 5 is:

Step-by-step solution

Let the nodes be numbered 1, 2, 3, 4, and 5 in order. The ideal wire connecting node 1 to node 4 makes them equipotential. Let this be node A. The ideal wire connecting node 2 to node 5 makes them equipotential. Let this be node B. Node 3 remains a distinct node, let's call it node C. Now map the resistors to these new nodes: R₁ is connected between node 1 (A) and node 2 (B). R₂ is connected between node 2 (B) and node 3 (C). R₃ is connected between node 3 (C) and node 4 (A). R₄ is connected between node 4 (A) and