Compute the equivalent capacitance between terminals A and B for the following network: A 1 F capacitor and a 2 F capacitor are joined at terminal A . Their respective other ends connect to intermediate junctions X and Y . From junction X , a 3 F capacitor connects to terminal B . From junction Y , a 6 F capacitor connects to terminal B . Finally, a 5 F capacitor bridges junctions X and Y .

Step-by-step solution

The given circuit represents a Wheatstone bridge. The ratio of capacitances in the arms connected to terminal A is C_ AX C_ AY = 1 2 . The ratio of capacitances in the arms connected to terminal B is C_ XB C_ YB = 3 6 = 1 2 . Since C_ AX C_ AY = C_ XB C_ YB , the Wheatstone bridge is balanced. Therefore, the potential at junction X is equal to the potential at junction Y, and no charge flows through the 5 F capacitor. It can be removed from the circuit. The equivalent capacitance of the upper branch ( 1 F and 3 F i