A bridge circuit has four nodes A, B, C, and D. The resistances of the branches are: R_ AB = 3 , , R_ BC = 3 , , R_ CD = 6 , , and R_ DA = 6 , . A branch containing a 24 V ideal DC source and a 4 , series resistor connects nodes A and C, with the positive terminal at A. A second branch containing an unknown ideal DC source E and a 4.5 , series resistor connects nodes B and D, with the positive terminal at B. If the n

Step-by-step solution

Using the superposition theorem, we analyse the circuit by considering one source at a time. Case 1: Only the 24 V source is active (the source E is replaced by a short circuit). The 24 V source is connected across nodes A and C. The bridge arms are R_ AB + R_ BC and R_ AD + R_ DC . The ratio of resistances is R_ AB R_ AD = 3 6 = 1 2 and R_ BC R_ DC = 3 6 = 1 2 . The bridge is balanced, so no current flows through the branch BD. The equivalent resistance of the bridge is: R_ eq1 = (3 + 3) , (6 + 6) , = 6 , 12 , = 4