Four resistors are connected to form a quadrilateral network ABCD . The resistances of the arms are R_ AB = 4 , , R_ BC = 8 , , R_ CD = 16 , , and R_ DA = 8 , . A fifth resistor of 20 , is connected between the junctions B and D . What is the equivalent resistance of this network between the terminals A and C ?

Step-by-step solution

The given circuit is a Wheatstone bridge network. Checking the balance condition of the Wheatstone bridge: R_ AB R_ AD = 4 8 = 1 2 R_ BC R_ CD = 8 16 = 1 2 Since R_ AB R_ AD = R_ BC R_ CD , the Wheatstone bridge is balanced. In a balanced Wheatstone bridge, the potentials at junctions B and D are equal. Therefore, no current flows through the 20 , resistor connected between them, and it can be removed from the circuit. The circuit simplifies to two parallel branches: Resistance of the upper branch, R₁ = R_ AB + R_