Five capacitors are connected to form a square network ABCD with a diagonal BD , as shown in the figure. The capacitances are C_ AB = 20 F , C_ BC = 5 F , C_ AD = 20 F , C_ DC = 5 F , and C_ BD = 15 F . What is the equivalent capacitance of the network between the terminals A and C ?

Step-by-step solution

The given circuit is a Wheatstone bridge. The condition for a balanced Wheatstone bridge is C_ AB C_ BC = C_ AD C_ DC . Substituting the given values: C_ AB C_ BC = 20 5 = 4 C_ AD C_ DC = 20 5 = 4 Since the bridge is balanced, the potentials at points B and D are equal ( V_B = V_D ). Therefore, no charge flows through the capacitor C_ BD , and it can be removed from the circuit. The circuit now consists of two parallel branches. Capacitors C_ AB and C_ BC are in series. Their equivalent capacitance is: C_ ABC = C_