Consider a ladder network that contains identical capacitors
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Consider a ladder network that contains n identical capacitors, each of capacitance C. The construction is as follows:
• Stage 1 — Capacitors 1 and 2 are connected in series between terminals A and B.
• Stage 2 — Capacitor 3 is connected in parallel with the series combination formed in Stage 1.
• Stage 3 — Capacitor 4 is connected in series with the entire grouping obtained after Stage 2.
• Stage 4 — Capacitor 5 is connected in parallel with the grouping obtained after Stage 3.
The pattern of alternating series and parallel additions continues until all n capacitors have been used.
(a) For the case n=3, show all steps in reducing the network to a single equivalent capacitance between A and B, and determine its numerical value in terms of C.
(b) Derive a general expression Ceq(n) for the equivalent capacitance of the ladder when n is an odd integer. Present your result in closed form using C and n.
(c) Determine the limit of Ceq(n) as n→∞ for the odd-integer sequence. Interpret the physical significance of this limit in the context of charge storage between A and B.
(d) Discuss whether the same limit would be reached if n were allowed to take even values, supporting your argument with an explicit calculation for n=4.