A uniform wire of total resistance 60 is bent into the shape of a circle. Four points A, B, C, and D are marked on the wire such that they divide the circumference into four equal arcs in clockwise order. A resistor of 50 is connected between points B and D. If a battery of 60 V is connected across points A and C, the total current supplied by the battery is ____ A.

Step-by-step solution

The total resistance of the wire is 60 . Since points A, B, C, and D divide the circle into four equal arcs, the resistance of each arc is: R_ AB = R_ BC = R_ CD = R_ DA = 60 4 = 15 The circuit forms a Wheatstone bridge between terminals A and C, with arms AB, BC, AD, and DC. The 50 resistor between B and D acts as the central arm. Checking the balance condition: R_ AB R_ BC = 15 15 = 1 R_ AD R_ DC = 15 15 = 1 Since the ratio is equal, the bridge is balanced and no current flows through the 50 resistor. The equival