In a circuit, an ideal 24 V battery is connected across nodes B and D, with node B at a higher potential. Four resistors are connected to form a bridge: R_ AB = 3 , , R_ AD = 6 , , R_ CB = 6 , , and R_ CD = 3 , . A branch containing a variable resistor R in series with a 12 V ideal battery is connected between nodes A and C. The positive terminal of this 12 V battery is connected to node C. The maximum possible power

Step-by-step solution

To find the maximum power, we first find the Thevenin equivalent of the circuit across nodes A and C (without the branch AC). Let V_D = 0 V , then V_B = 24 V . The potential at node A is V_A = 24 6 3+6 = 16 V . The potential at node C is V_C = 24 3 6+3 = 8 V . The Thevenin voltage V_ th across A and C is V_A - V_C = 16 - 8 = 8 V (with A at a higher potential). The Thevenin resistance R_ th is found by shorting the 24 V battery: R_ th = (R_ AB R_ AD ) + (R_ CB R_ CD ) = (3 6) + (6 3) = 2 + 2 = 4 , . The equivalent c