Two conductors are made from the same material and are of the same length but one has a circular cross sectional area with diameter 1.2 mm and the other is square with 0.6 mm on each side.What is the ratio R_circular/R_square of their resistances?

Question

Quizplus · Accepted Answer

The resistance of a conductor depends on its cross-sectional area as well as its length and material. The resistance is inversely proportional to the cross-sectional area. Let's denote the resistance of the circular conductor as RC and that of the square conductor as RS. We know that both conductors are of the same material and length, so their resistance depends only on their cross-sectional areas. The circular conductor has a diameter of 1.2 mm, so its radius is 0.6 mm. Its cross-sectional area is given by: AC = πr^2 = π(0.6 mm)^2 = 1.13 mm^2 The square conductor has a side length of 0.6 mm, so its cross-sectional area is: AS = (0.6 mm)^2 = 0.36 mm^2 The ratio of their resistances is: RC/RS = AS/AC = 0.36/1.13 = 1/π So, RS/RC = π. Therefore, the answer is B: R_circular/R_square = 1/π.

Two Conductors Are Made from the Same Material and Are π\piπ

Two Conductors Are Made from the Same Material and Are $\pi$