A uniform conducting wire having an initial resistance of 3 is stretched to three times its original length. The stretched wire is then bent to form a closed equilateral triangle. The equivalent resistance between any two vertices of this triangle is

Step-by-step solution

When a wire is stretched to n times its original length, its volume remains constant, and its new resistance becomes R_ new = n^2 R₀ . Here, n = 3 and R₀ = 3 . R_ new = (3)^2 3 = 27 . The wire is bent into an equilateral triangle, which consists of three equal sides. The resistance of each side is: R_ side = 27 3 = 9 . When calculating the equivalent resistance between any two vertices, one side of the triangle is in parallel with the series combination of the other two sides. Resistance of the two sides in series