A uniform wire has a resistance of 18 at 0^ C . The temperature coefficient of resistance of the material of the wire is 5 10⁻³ ^ C ⁻¹ . The wire is bent to form an equilateral triangle and the entire arrangement is kept at a temperature of 100^ C . The equivalent resistance across any two vertices of the triangle at this temperature is _____ .

Step-by-step solution

First, we find the total resistance of the wire at 100^ C . R_ T = R₀(1 + T) R₁₀₀ = 18(1 + 5 10⁻³ 100) R₁₀₀ = 18(1 + 0.5) = 27 The wire is bent into an equilateral triangle, so it is divided into three equal parts. The resistance of each side of the triangle at 100^ C is: R_ side = 27 3 = 9 Across any two vertices, one side is in parallel with the series combination of the other two sides. Resistance of the series combination = 9 + 9 = 18 . The equivalent resistance R_ eq is: R_ eq = 9 18 9 + 18 = 162 27 = 6 . Answ