Twelve capacitors, each having capacitors, `C`, are joined to from a cube as shown. Find the equivalent capacitance between the ends of
(a) Digitonal i.e., between `A` and `B`.
(b) Face diagonal i.e., between `A` and `C`.
(c) side of cube i.e., between `A` and `D`.

Explanation

(a) `{:(,D,H,F,C,E,G),(A,1,1,1,2,2,2),(B,2,2,2,1,1,1):}`
`(D,H,F),(C,E,G)` are at same potential, redraw the diagram.

(b)
`{:(,D,E,G,H,B,F),(A,1,2,2,1,3,1),(C,1,2,2,1,1,3):}`
`(D,E),(G,H)` are at same potential, remove capacitors betweem `D` and `E,G` and `H`.

(c) `{:(,C,E,F,H,B,G),(A,2,2,1,1,3,2),(D,1,1,2,2,2,3):}`
`(C,E),(F,H)` are at same potential, redraw the diagram.


`C_(eq)=(5C)/(7)+C=(12C)/(7)`