Circuit with Capacitors and a Battery 1 2 3 4 5 6 7 A circuit is constructed wit

Question

Circuit with Capacitors and a Battery

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A circuit is constructed with five capacitors and a battery as shown. The values for the capacitors are: C1 = C5 = 3.5 F, C2 = 2.8 F, C3 = 6.4 F, and C4 = 2.8 F. The battery voltage is V = 12 V.

1)

What is Cab, the equivalent capacitance between points a and b?

F

2)

What is Cac, the equivalent capacitance between points a and c?

F

3)

What is Q5, the charge on capacitor C5?

C

4)

What is Q2, the charge on C2?

C

5)

What is Q1, the charge on capacitor C1?

C

6)

What is V4, the voltage across capacitor C4?

V

Explanation / Answer

1) C23 = C2*C3/(C2 + C3) ======> Cab = C4 + (C2*C3/(C2 + C3))

Cab = 2.8 + (2.8*6.4/(2.8 + 6.4)) = 2.8 + 1.95 = 4.75 F

2) Cac = C1*Cab/(C1 + Cab) = 3.5*4.75/(3.5 + 4.75) = 2.02 F

3) Ceq = C5*Cac/(C5 + Cac) = 3.5*2.02/(3.5 + 2.02) = 1.28 F

Q5 = Ceq*V = 1.28*12 = 15.36 C

4) Vab = V – 2Vbc = V – 2(Q5/C5) = 12 – 2(15.36/3.5) = 3.22 V

Vab = (Q2/C2) + (Q2/C3) =======> Q2 = Vab*(C23) = 3.22*1.95 = 6.3 C

5) Q1 = Q5 = 15.36 C

6) V4 = Vab = 3.22 V

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