An infinite number of identical capacitors each of capacitance `1 mF` are connected as shown in the figure. Then the equivalent capacitance between `A` and `B` is.
.

Options

A. `1muF`
B. `2muF`
C. `1/2muF`
D. `infty`

Answer

B

Explanation

b) this combination forms a GP, `s=1+1/2+1/4+1/8 + ...`
Sumof infinite GP,
`S=(a/(1-r))`
`s= 1/(1-1/2)`
`s=1/(1/2)`
`s=2`
`therefore` Hence, capacitance, of the combination
`C_(infty) = 2 x 1muF=2muF`