In the figure (Figure 1) , C1 = C5 = 8.3 ?F and C2= C3= C4 = 4.2 ?F . The applied potential is Vab = 250 V .
A)Find Q1 Q2 Q3 Q4 Q5
B) Find V1 V2 V3 V4 V5
C_{3} and C_{4} are in series and their series combination is given as
C_{34} = C_{3} C_{4} /(C_{3} + C_{4}) = (4.2 x 4.2)/(4.2 + 4.2) = 2.1 uF
C_{34} and C_{2} are in parallel and their parallel combination is given as
C_{234} = C_{2} + C_{34} = 4.2 + 2.1 = 6.3 uF
C_{1} , C_{234} and C_{5} are in series and their series combination is given as
1/C_{12345} = 1/C_{1} + 1/C_{234} + 1/C_{5}
1/C_{12345} = 1/8.3 + 1/6.3 + 1/8.3
C_{12345} = 2.5 uF
Q_{total} = C_{12345} V_{ab} = 2.5 x 250 = 625 uC
Q_{1}= Q_{5} = Q_{total} = 625 uC since C_{1} and C_{5} are in series with V_{ab}
V_{1} = V_{5} = Q_{1}/C_{1} = 625 / 8.3 = 75.3 volts
V_{2} = V_{ab} - V_{1} - V_{5} = 250 - 75.3 - 75.3 = 99.4 volts
Q_{2} = C_{2} V_{2} = 4.2 x 99.4 = 417.5 uC
Q_{3} = Q_{4} = Q_{total} - Q_{2} = 625 - 417.5 = 207.5 uC
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