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

`C_(1),C_(2),C_(3)` are in series,
`therefore (1)/(C_(S))=(1)/(C)+(1)/(2C)+(1)/(3C)`
`=(6+3-2)/(6C)=(11)/(6C)`
`therefore C_(S)=(6C)/(11)`
When the capacitors are in series, each capacitor has the same charge.
Thus, `q_(1)=q_(2)=q_(3)=C_(S)xxV=(6CV)/(11)`
and the charge on `C_(4)` is `Q_(4)=(4C)V=4CV`
`therefore (q_(2))/(q_(4))=(6CV)/(11)xx(1)/(4CV)=(3)/(22)`.