A uniform wire of initial resistance 4 is stretched uniformly to 3 times its original length. The stretched wire is then bent into a complete circle. The equivalent resistance between two points on the circumference that subtend an angle of

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A uniform wire of initial resistance 4 is stretched uniformly to 3 times its original length. The stretched wire is then bent into a complete circle. The equivalent resistance between two points on the circumference that subtend an angle of 60^ at the center is

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Correct answer: B. 5

When a wire is stretched uniformly, its volume remains constant. If the length becomes n times its original value, the cross-sectional area becomes 1 n times. The new resistance R_ new is given by: R_ new = nL A/n = n^2 ( L A ) = n^2 R₀ Given n = 3 and R₀ = 4 : R_ new = 3^2 4 = 36 The wire is bent into a circle. Two points subtending 60^ at the center divide the circle into two arcs. The fractions of the total circumference are: f₁ = 60^ 360^ = 1 6 f₂ = 360^ - 60^ 360^ = 5 6 The resistances of the two parts are: R₁

A uniform wire of initial resistance 4 is stretched uniformly to 3 times its original length. The stretched wire is then bent into a complete circle. The equivalent resistance between two points on the circumference that subtend an angle of 60^ at the center is

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