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

Options

A. `1 muF`
B. `2 muF`
C. `(1)/(2) muF`
D. `oo`

Answer

B

Explanation

In each row, Fig, the capacitance are in series, and different rows of capacitance are joined in parallel. Therefore, total capacity
`C = C + (C )/(2) + (C )/(4) + (C )/(8) + (C )/(16) + …… oo`
`= C [1 + (1 )/(2) + (1)/(4) + (1)/(8) + (1)/(16) + …… oo]`
`= C [(1)/(1-1//2)] = 2C = 2 muF`