A Wheatstone bridge ABCD has arms with resistances AB = 2 , BC = R , AD = 4 , and DC = R' . A 30 V battery is connected across terminals A and C along with an ammeter in series. The ammeter reads a total current of 5 A drawn from the battery. If a galvanometer connected between B and D shows zero deflection, the value of resistance R (in ) is

Step-by-step solution

Let the equivalent resistance of the entire circuit be R_ eq . From Ohm's law, the total equivalent resistance is: R_ eq = V I = 30 5 = 6 Since the galvanometer shows zero deflection, the Wheatstone bridge is balanced. The balancing condition is: R_ AB R_ BC = R_ AD R_ DC 2 R = 4 R' R' = 2R The equivalent resistance of the balanced bridge is the parallel combination of the series arms (AB + BC) and (AD + DC) : R_ eq = (R_ AB + R_ BC )(R_ AD + R_ DC ) (R_ AB + R_ BC ) + (R_ AD + R_ DC ) Substitute R' = 2R into the e