As shown in the figure, a finite ladder is assembled by connecting several sections of 2 F and 4 F capacitor combinations. The ladder is terminated by a capacitor of capacitance C . Determine the value that should be chosen for C so that the equivalent capacitance of the ladder between points A and B remains independent of the number of sections.

Step-by-step solution

For the equivalent capacitance of the ladder between points A and B to be independent of the number of sections, the equivalent capacitance of the entire ladder must be equal to the terminating capacitance C . Let the equivalent capacitance of the ladder be C_ eq . By observing the repeating unit of the circuit from the terminals A and B, the ladder consists of a 2 F capacitor in parallel with the series combination of a 4 F capacitor and the rest of the ladder. Thus, the equivalent capacitance is given by: C_ eq =