The figure shows a 12.7 V battery and four uncharged capacitors of capacitances

Question

The figure shows a 12.7 V battery and four uncharged capacitors of capacitances C1 = 1.09 ?F,C2 = 2.39 ?F,C3 = 3.01 ?F, and C4 = 4.19 ?F.
(a) If only switch S1 is closed, what is the charge (in C) on capacitor 3?
(b) If both switches are closed, what is the charge (in C) on capacitor 3?

The figure shows a 12.7 V battery and four uncharged capacitors of capacitances C1 = 1.09 ?F,C2 = 2.39 ?F,C3 = 3.01 ?F, and C4 = 4.19 ?F. If only switch S1 is closed, what is the charge (in C) on capacitor 3? If both switches are closed, what is the charge (in C) on capacitor 3?

Explanation / Answer

a)

C13 =C1*C3/(C1+C4) =(1.09*3.01)/(1.09+3.01)

C13 =0.8 uF

C24 =C2*C3/(C2+C4) =2.39*4.19/(2.39+4.19)

C24 =1.52 uF

V13 =V24 =12.7 V

Q3 =Q13 =V13*C13 =12.7*0.8

Q3 =10.16 uC

b)

C12 =C1+C2 =1.09+2.39

C12 =3.48 uF

C34 =C4+C3 =3.01+4.19

C34=7.2 uF

V34 =V*(C12/C12+C34) =12.7*(3.48/3.48+7.2)

V34 =4.14 V

Q3=V34*C3 =4.14*3.01

Q3 =12.46 uC

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