A network of four capacitors of capacity equal to `C_(1) = C, C_(2) = 2C, C_(3) = 3C` and `C_(4) = 4C` are connected to a battery as shown in the figure. The ratio o fthe charges on `C_(2)` an `C_(4)` is

Options

A. `4//7`
B. `3//22`
C. `7//4`
D. `22//3`

Answer

B

Explanation

Here, `C_(1), C_(2), C_(3)` are in series, Fig.
`(1)/(C_(s)) = (1)/(C_(1)) + (1)/(C_(2)) + (1)/(C_(3)) = (1)/( C) + (1)/(2C) + (1)/(3C) = (11)/(6C)`
`C_(s) = (6C)/(11)`
The combination is in parallel with `C_(4)`.
`("Charge on "C_(2) (or C_(1) or C_(3)))/("Charge on "C_(4)) = (C_(s) xx V)/(C_(4) xx V)`
`= (6C//11)/(4C) = (3)/(22)`