The capacitors
1.00 μF
and
5.00 μF
are connected in series combination. The equivalent capacitance is,
Cpt=C1.00 μFC5.00 μFC1.00 μF+C5.00 μF
The capacitors
8.00 μF
and
4.00 μF
are connected in series combination. The equivalent capacitance is,
Cpb=C8.00 μFC4.00 μFC8.00 μF+C4.00 μF
The capacitances
Cpt
and
Cpb
are in parallel combination. The total equivalent capacitance is,
Ceq=Cpt+Cpb
Therefore,
Ceq=(C1.00 μFC5.00 μFC1.00 μF+C5.00 μF)+(C8.00 μFC4.00 μFC8.00 μF+C4.00 μF)
Substitute
1.00 μF
for
C1.00 μF
,
5.00 μF
for
C5.00 μF
,
8.00 μF
for
C8.00 μF
and
4.00 μF
for
C4.00 μF
Ceq=[(1.00 μF)(5.00 μF)(1.00 μF)+(5.00 μF)]+[(8.00 μF)(4.00 μF)(8.00 μF)+(4.00 μF)]=4.00 μF
Formula to calculate the total charge is,
Qtotal=CeqV
Substitute
4.00 μF
for
Ceq
and 24.0 V for V.
Qtotal=(4.00 μF)(24.0 V)=96.0 μC
Formula to calculate the charge on
1.00 μF
capacitor is,
Q1=C1.00 μF(QtotalC1.00 μF+C5.00 μF)
Substitute
96.0 μC
for
Qtotal
,
1.00 μF
for
C1.00 μF
and
5.00 μF
for
C5.00 μF
Q1=(1.00 μF)(96.0 μC(1.00 μF)+(5.00 μF))=16.0 μC
Formula to calculate the charge on
5.00 μF
capacitor is,
Q2=C5.00 μF(QtotalC1.00 μF+C5.00 μF)
Substitute
96.0 μC
for
Qtotal
,
1.00 μF
for
C1.00 μF
and
5.00 μF
for
C5.00 μF
Q2=(5.00 μF)(96.0 μC(1.00 μF)+(5.00 μF))=80.0 μC
Formula to calculate the charge on
8.00 μF
capacitor is,
Q3=C8.00 μF(QtotalC8.00 μF+C4.00 μF)
Substitute
96.0 μC
for
Qtotal
,
8.00 μF
for
C8.00 μF
and
4.00 μF
for
C4.00 μF
Q3=(8.00 μF)(96.0 μC(8.00 μF)+(4.00 μF))=64.0 μC
Formula to calculate the charge on
4.00 μF
capacitor is,
Q4=C4.00 μF(QtotalC8.00 μF+C4.00 μF)
Substitute
96.0 μC
for
Qtotal
,
8.00 μF
for
C8.00 μF
and
4.00 μF
for
C4.00 μF
Q4=(4.00 μF)(96.0 μC(8.00 μF)+(4.00 μF))=32.0 μC
Conclusion:
The charge on
1.00 μF
capacitor is
16.0 μC
The charge on
5.00 μF
capacitor is
80.0 μC
The charge on
8.00 μF
capacitor is
64.0 μC
The charge on
4.00 μF
capacitor is
32.0 μC