A uniform resistance wire is bent into a complete circle of circumference L . A battery is connected across two points A and C on the circle such that the minor arc AC has a length of L 3 . A galvanometer is connected between a point B (located on the minor arc AC ) and a point D (located on the major arc AC ). If the length of the arc AB is L 12 and the galvanometer shows zero deflection, the length of the arc AD is

Step-by-step solution

The resistance of any part of the uniform wire is proportional to its arc length. The battery is connected across points A and C . The minor arc AC has length L 3 , so the major arc AC has length L - L 3 = 2L 3 . Point B is on the minor arc AC . The length of arc AB is L 12 . The length of arc BC is L 3 - L 12 = 3L 12 = L 4 . The ratio of resistances in the minor arc branch is: R_ AB R_ BC = L/12 L/4 = 1 3 For the galvanometer connected between B and D to show zero deflection, the Wheatstone bridge formed by the ar