A circuit is constructed with five capacitors and a battery as shown. The values

Question

A circuit is constructed with five capacitors and a battery as shown. The values for the capacitors are: C1 = C5 = 4.3 F, C2 = 3 F, C3 = 6.8 F, and C4 = 3.6 F. The battery voltage is V =12 V.

1) What is Cab, the equivalent capacitance between points a and b? F Submit

2) What is Cac, the equivalent capacitance between points a and c? F Submit

3) What is Q5, the charge on capacitor C5? C Submit

4) What is Q2, the charge on C2? C Submit

5) What is Q1, the charge on capacitor C1? C Submit

6) What is V4, the voltage across capacitor C4?

Explanation / Answer

Given :-

C1 = C5 = 4.3 F,

C2 = 3 F,

C3 = 6.8 F,

C4 = 3.6 F

V =12 V

1)

C23 = C2C3 / (C2 + C3)

Cab = C4 + C2C3 / (C2 + C3)

Cab = 3.6 + (3 x 6.8) / (3 + 6.8)

Cab = 5.68 F

2)

Cac = C1Cab / (C1 + Cab)

Cac = (4.3 x 5.68) / (4.3 + 5.68)

Cac = 2.447 F

3)

Ceq = C5Cac / (C5 + Cac)

Ceq = (4.3 x 2.447) / (4.3 + 2.447)

Ceq = 1.56 F

Q5 = V x Ceq

Q5 = 12 x 1.56

Q5 = 18.72 C

4)

Vab = V - 2Vc = V - 2(Q5/C5)

Vab = 12 - 2(18.72/4.3)

Vab = 3.3 V

Vab = Q2 / C2 + Q2 / C3

Q2 = Vab x C2C3 / (C2 + C3)

Q2 = 3.3 x 2.08

Q2 = 6.87 C

5)

Q1 = Q5 = 18.72 F

6)

V4 = Vab = 12V - 8.7 = 3.3 V

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