A uniform wire of resistance 36 is bent into a circle with centre O. A straight wire of resistance 12 is connected between two diametrically opposite points A and B on the circle. A battery of EMF 72 V and zero internal resistance is connected across two points C and D on the circle. Points C and D lie on opposite sides of the diameter AB such that AOC = 60^ and AOD = 60^ . The total current drawn from the battery is

Step-by-step solution

The uniform circular wire has a total resistance of 36 . The resistance per unit angle is 36 360^ = 0.1 /^ . The points C and D divide the circle into four arcs. Based on the given angles, the resistances of these arcs are: R_ CA = 60^ 0.1 = 6 R_ AD = 60^ 0.1 = 6 Since A and B are diametrically opposite, AOB = 180^ . R_ CB = (180^ - 60^ ) 0.1 = 120^ 0.1 = 12 R_ DB = (180^ - 60^ ) 0.1 = 120^ 0.1 = 12 The straight wire between A and B has a resistance R_ AB = 12 . The battery is connected across C and D. The circuit