The switch S in the circuit shown below has been open for a long time when, at t

Question

The switch S in the circuit shown below has been open for a long time             when, at time t = 0, it is closed.  The values of the circuit elements             are:  V = 12 V,             R1 = 110 ?,             R2 = 220 ?,             R3 = 330 ?,             C1 = 40 ?F and             C2 = 80 ?F.

the switch is closed?             Q2final =                      C           

The switch S in the circuit shown below has been open for a long time when, at time t = 0, it is closed. The values of the circuit elements are: V = 12 V, R1 = 110 ?, R2 = 220 ?, R3 = 330 ?, C1 = 40 ?F and C2 = 80 ?F. the switch is closed? Q2final =

Explanation / Answer

After the switch has been closed for long time both capacitors act as open circuit ,so current in the circuit is

I =V/(R1+R2) =12/(110+220)

I=0.03636 A

Voltage across R2 is

V2 =I*R2 =0.03636*220 =8 V

after long time capacitors are fully charged and no current flowing through R3.

Applying KVL to right side loop

Vc1 +Vc2-V2=0

since both capacitors are in series

Qc1 =Qc2 =Q

Q/C1 +Q/C2 =V2

Q(1/40u +1/80u) =8

Q*37500 =8

Q=2.13*10^-4 C

Q2,final = 2.13*10^-4 C or 213.33 uC

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