A wire possessing a resistance of 15.0 is bent into a regular hexagon ABCDEFA . Find the equivalent resistance of the loop between points A and C .

Step-by-step solution

Total resistance of the wire, R = 15.0 Since the wire is bent into a regular hexagon, it has 6 equal sides. Resistance of each side = 15.0 6 = 2.5 The equivalent resistance is to be found between points A and C . The hexagon can be divided into two parallel paths between A and C : Path 1: A B C ( 2 sides) Resistance of Path 1, R₁ = 2 2.5 = 5.0 Path 2: A F E D C ( 4 sides) Resistance of Path 2, R₂ = 4 2.5 = 10.0 Since R₁ and R₂ are in parallel, the equivalent resistance R_ eq is: R_ eq = R₁ R₂ R₁ + R₂ = 5.0 10.0 5.0