In figure, battery B supplies `12 V`. Find the charge on each capacitor

(a) first when only switch S1 is closed and
(b) later when S2 is also closed.
(Take `C_1=1.0muF, C_2=2.0muF, C_3=3.0muF` and `C_4=4.0muF)`

Answer

A, C, D

Explanation

a.

`C_13 =(1xx3)/(1+3)=3/4muF`
`C_24=(2x4)/(2+4)=4/3muF`
`V_(C_1C_3)=V_(C_2C_3)=12V`
`:. q_1=q_3=(C_13)(V_(C_1C_3)=3/4xx12)=9muC`
`q_2=q_4=(C_24)(V_(C_2C_4)=4/3xx12)=16muC`
b.

`C_12=(1xx2)/(1+2)=2/3muF`
`C_34=(3xx4)/(3+4)=12/7muF`
`V_1/V_2=C_34/C_12=(12/7)/(2/3)=18/7`
`:. V_1=(18/25)(12)=8.64V`
V_2=12-8.64=3.36V`
now, we can apply q=CV for finding charge on different capacitors.