A wire of resistance 15.0 is bent to form a regular hexagon ABCDEFA . Determine the equivalent resistance of the loop between points A and B .

Step-by-step solution

Total resistance of the wire is 15.0 . Since the wire is bent into a regular hexagon, it has 6 equal sides. The resistance of each side is R = 15.0 6 = 2.5 . The points A and B are adjacent vertices. The equivalent circuit consists of two parallel paths between A and B : 1. The direct path along the side AB with resistance R₁ = R = 2.5 . 2. The path through the remaining five sides with resistance R₂ = 5R = 12.5 . The equivalent resistance R_ eq is given by the parallel combination of R₁ and R₂ : R_ eq = R₁ R₂ R₁ +