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

c.When steady state is reached, the current I from the battery is
`9 = I(3+6) or I=IA`
Potential difference across `3Omega` resistance is 3 V and potential difference across
`6Omega` resistance is 6 V.
Potential difference across
`3muF` capacitor is 3V and pd
across `6muF` capacitor is 6 V.
Therefore, charge on `3muF`
capacitor is
`Q_1 = 3 xx 3 = 9muC`

Charge on `6muF` capacitor is
`Q_2 = 6 xx 6 = 36 muC`
Charge `(-Q_1)` is shifted from the positive plate of `6muF` capacitor.
The remaining charge on the positive plate of `6muF` capacitor is
shifted through the switch. Therefore, charge passing through
the switch is `36-9 = 27muC` .