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) The total charge enclosed in the dotted portion when the switch S is open is zero. When the switch is closed
and steady is reached, the current I coming from
the battery is
`9 = I (3+6) rArr I = 1A`

`:. Potential difference across `3Omega` resistance = 3V and
potential difference across `6Omega` resistance = 6V
`:. p.d. across 3`muF` capacitor = 3V
and p.d. across 6 `muF` capacitor = 6V.
`:. Charge on `3muF` capcitor `Q_1 = 3 xx 3 = 9muC`
Charge on `6muF` capacitor `Q_2 = 6 xx 6 = 36 mu C`
The total charge enclosed in the dotted portion =
`:. Charge passing the switch = 36-9 = 27 muC`