A bridge circuit has four nodes P, Q, R, and S. The resistances of the branches are: R_ PQ = 6 , , R_ QR = 6 , , R_ RS = 12 , , and R_ SP = 12 , . A branch containing a 30 V ideal battery and a 2 , series resistor connects nodes P and R. A second branch containing a 24 V ideal battery and a 3 , series resistor connects nodes Q and S. What is the total electrical power dissipated in the entire circuit?

Step-by-step solution

Using the superposition theorem, we can analyse the circuit by considering one source at a time. Case 1: Only the 30 V source is active (the 24 V source is replaced by a short circuit). The 30 V source is connected across nodes P and R. The bridge arms are R_ PQ + R_ QR and R_ SP + R_ RS . The ratio of resistances for the left and right paths from P to R is R_ PQ R_ SP = 6 12 = 1 2 and R_ QR R_ RS = 6 12 = 1 2 . Since the bridge is balanced, no current flows through the branch QS. The equivalent resistance of the b