Determine the equivalent capacitance between points A and B for the infinite ladder circuit illustrated in the figure.

Step-by-step solution

Let the equivalent capacitance between points A and B be C_ eq . Because the ladder is infinite, the circuit to the right of the first 2 F capacitor is identical to the entire circuit and thus has an equivalent capacitance of C_ eq . The circuit can be simplified to a 1 F capacitor in parallel with the series combination of a 2 F capacitor and C_ eq . The equivalent capacitance is given by: C_ eq = 1 + 2 C_ eq 2 + C_ eq Multiplying both sides by (2 + C_ eq ) : C_ eq (2 + C_ eq ) = 1(2 + C_ eq ) + 2C_ eq 2C_ eq + C_