a)
C_{3} and C_{5} are in series and their combination is given as
C_{35} = C_{3} C_{5}/(C_{3} + C_{5}) = (4.5) (4.5)/(4.5 + 4.5) = 2.25 uF
C_{2} , C_{4} and C_{35} are in parallel and their combination is given as
C_{2345} = C_{2} + C_{4} + C_{35} = 1.8 + 1.8 + 2.25 = 5.85 uF
C_{1} and C_{6} are in parallel and their combination is given as
C_{16} = C_{1} + C_{6} = 5 + 5 = 10 uF
C_{16} and C_{2345} are in series and their combination is given as
C_{eq} = C_{16} C_{2345} /(C_{16} + C_{2345} )
C_{eq} = (10) (5.85) /(10 + 5.85)
C_{eq} = 3.7 uF
b)
Q = charge stored by the combination of capacitors
V = battery Voltage = 27 Volts
Charge stored is given as
Q = C_{eq} V
Q = (3.7) (27)
Q = 99.9 uC
c)
V_{1} = Voltage across C_{1} = V_{16} = Voltage across the combination of C_{1} and C_{6} (Since in parallel voltage remain the same)
Q_{1} = charge in C_{1} = Q_{16} = charge in C_{16} = Q = 99.9 uC (Since charge remain same in series)
Using the equation
Q_{1} = C_{1} V_{1}
99.99 = (5) V_{1}
V_{1} = 19.98 Volts
d)
Q_{1} = charge in C_{1} = Q_{16} = charge in C_{16} = Q = 99.9 uC
e)
V_{2} = Voltage across C_{2} = Voltage across the parallel combination C_{2345} = V - V_{16} = 27 - 19.98 = 7.02 Volts (Since in parallel voltage remain the same)
f)
Q_{2} = charge in C_{2} = ?
Using the equation
Q_{2} = C_{2} V_{2}
Q_{2} =(1.8) (7.02)
Q_{2} = 12.6 uC
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