A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is
.

Options

A. 0
B. `54muC`
C. `27muC`
D. `81muC`

Answer

C

Explanation

When switch is open total charge enclosed in the dotted portion is zero.

Because `Q_(1)=Q_(2)`
When the switch is closed and steady state is reached -
`I=(9)/(3+6)=1A`
Potential difference across `3Omega` resistor or `3muF` capacitor = 3V
Potential difference across `6Omega` resistor or `6muF` capacito = 6V
`Q_(1)=C_(1)V_(1)=3xx3=9muC`
`Q_(2)=C_(2)V_(2)=6xx6=36muC`
The total charge enclosed in the dotted portion = charge passing the switch `=36-9=27muC`.