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) C234 = [2.8 * 6.4 / (2.8 + 6.4)] + 2.8 = 4.75 muF

capacitance across ab = 4.75 muF

2) C1234 = 1 / [1/4.75 + 1/3.5] = 2.015 muF

capacitance across ac = 2.015 muF

3) C12345 = 1 / [1/2.015 + 1/3.5] = 1.28 muF

charge on capacitor C5 , Q5 = 1.28 * 12 = 15.35 muC

5) charge on capacitor C1 , Q1= 15.35 muC

6) voltage across capacitor C4, V4 = 15.35 / 4.75 = 3.23 V

4) Charge on C2, Q2 = C2 V2 = 2.8 * 3.23 = 9 muC

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