Question

$12$ number of capacitors each of capacity $C$ are arranged along sides of a cube as shown in the figure. The equivalent capacity between points A and B is :

• A. $\frac{5}{6}C$
• B. $\frac{6}{5}C$
• C. $C$
• D. $30C$

Answer 1

The correct option is B $\frac{6}{5}C$

$⟹$ Observe that the three vertices adjacent to one of connection points of your grid always have the same potential, due to symmetry. Since they do, you can fuse them all together into one. The same goes for the other three vertices adjacent to the other connection point.
Now, you have reduced the problem into simple configuration $:\left(C||C||C\right)+\left(C||C||C||C||C||C\right)+\left(C||C||C\right)=3C+6C+3C=6/5C$
Here $+$ means serial connection an $||$ means parallel connection.