A circuit consists of a bridge network of five resistors connected between four nodes A, B, C, and D. The resistances are R_ AB = 5 , R_ BC = 10 , R_ AD = 10 , R_ DC = 20 , and R_ BD = 50 . This bridge network, taken across nodes A and C, is connected in series with an unknown resistor R and an ideal battery of 60 V . If the total current drawn from the battery is 4 A , the value of R is

Step-by-step solution

The given bridge network is connected across nodes A and C. The ratio of resistances in the adjacent arms is: R_ AB R_ BC = 5 10 = 1 2 R_ AD R_ DC = 10 20 = 1 2 Since R_ AB R_ BC = R_ AD R_ DC , the bridge is a balanced Wheatstone bridge. Therefore, no current flows through the resistor R_ BD = 50 , and it can be removed from the circuit. The equivalent resistance of the bridge network R_ bridge is the parallel combination of the series branches ABC and ADC: R_ ABC = 5 + 10 = 15 R_ ADC = 10 + 20 = 30 R_ bridge = 15