Question

Find the equivalent capacitance in C of the circuit between point $A$ and $B$.

Answer 1

Due to symmetry of the arrangement, the potential difference across the vertical capacitor arm $C$ is $zero$. SO these capacitors can be neglected.

Now, the total capacitance of upper branch between A and B is $\frac{1}{C_1}=\frac{1}{C}+\frac{1}{2C}+\frac{1}{4C}+\frac{1}{8C}+...\Rightarrow C_1=C/2$

similarly, total capacitance of lower branch between A and B is $C_2=C/2$

These two capacitance are in parallel, so total capacitance is $C_1+C_2=C$