Question

What is equivalent capacitance of the circuit between points A and B? 

• A. (2)/(3)μF
• B. (4)/(3)μF
• C. Infinite
• D. (1+√(3))μF

Hint:

For infinite capacitor ladders, use self-similarity: assume the remaining network has the same equivalent capacitance as the whole.

Answer 1

The Correct Option is D

Step 1: The given network is an infinite ladder of capacitors with repeating sections.

Step 2: Let the equivalent capacitance between A and B be C. 

Step 3: Due to self-similarity, removing the first section leaves the same equivalent capacitance C.

Step 4: Writing the equivalent capacitance equation and solving the resulting quadratic gives: C = (1+√(3))μF