Basic Physics

# Series and parallel capacitors circuits – problems and solutions

1. What is the total charges in the capacitor circuits below (1 μF = 10-6 F)

Known :

Capacitor 1 (C1) = 3 μF

Capacitor 2 (C2) = 3 μF

Capacitor 3 (C3) = 3 μF

Capacitor 4 (C4) = 2 μF

Capacitor 5 (C5) = 3 μF

Voltage (V) = 3 Volt

Wanted : Total charge in capacitor circuits (Q)

Solution :

The equivalent capacitor

Capacitor C1, C2 and C3 are connected in series. The equivalent capacitor :

1/C123 = 1/C1 + 1/C2 + 1/C3 = 1/3 + 1/3 + 1/3 = 3/3

C123 = 3/3 = 1 μF

Capacitor C123 and C4 are connected in parallel. The equivalent capacitor :

C1234 = C123 + C4 = 1 + 2 = 3 μF

Capacitor C1234 and C5 are connected in series. The equivalent capacitor :

1/C = 1/C1234 + 1/C5 = 1/3 + 1/3 = 2/3

C = 3/2 μF

C = 3/2 x 10-6 F

The total charges :

The total charges in the equivalent capacitor = the total charges in capacitor circuits :

Q = V C = (3 Volt)(3/2 x 10-6 Farad) = 9/2 x 10-6 Coulomb

Q = 9/2 microCoulomb = 9/2 μC

Q = 4.5 μC

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2. If C1 = C2 = 2 μF, C3 = C4 = 1 μF and C5 = 4 μF, determine the total charges in the capacitor circuits as shown in figure below (1 μF = 10-6 F)

Known :

Capacitor 1 (C1) = 2 μF

Capacitor 2 (C2) = 2 μF

Capacitor 3 (C3) = 1 μF

Capacitor 4 (C4) = 1 μF

Capacitor 5 (C5) = 4 μF

Voltage (V) = 1.5 Volt

Wanted : The total charges in circuits (Q)

Solution :

The equivalent capacitor :

Capacitor C3 and C4 are connected in parallel. The equivalent capacitor :

C34 = C3 + C4 = 1 + 1 = 2 μF

Capacitor C5, C1, C2 and C34 are connected in series. The equivalent capacitor :

1/C = 1/C5 + 1/C1 + 1/C2 + 1/C34

1/C = 1/4 + 1/2 + 1/2 + 1/2

1/C = 1/4 + 2/4 + 2/4 + 2/4

1/C = 7/4

C = 4/7 μF

C = 4/7 x 10-6 F

The total charges :

The total charges in the equivalent capacitor = the total charges in capacitor circuits :

Q = V C = (1.5 Volt)(4/7 x 10-6 Farad) = 6/7 x 10-6 Coulomb

Q = 6/7 microCoulomb

Q = 6/7 μC

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3. Determine the total charges in the capacitor circuits as shown in figure below.

Known :

Capacitor 1 (C1) = 3 μF

Capacitor 2 (C2) = 3 μF

Capacitor 3 (C3) = 4 μF

Capacitor 4 (C4) = 4 μF

Capacitor 5 (C5) = 8 μF

Voltage (V) = 10 Volt

Wanted : The total charge in the circuits (Q)

Solution :

The equivalent capacitor :

Capacitor C1 and C2 are connected in parallel. The equivalent capacitor :

C12 = C1 + C2 = 3 + 3 = 6 μF

Capacitor C3 and C4 are connected in series. The equivalent capacitor :

1/C34 = 1/C3 + 1/C4 = 1/4 + 1/4 = 2/4

C34 = 4/2 = 2 μF

Capacitor C12, capacitor C34 and capacitor C5 are connected in parallel. The equivalent capacitor :

C = C12 + C34 + C5 = 6 + 2 + 8 = 16 μF = 16 x 10-6 Farad

The total electric charges :

The total charges in the equivalent capacitor = the total charges in capacitor circuits :

Q = V C = (10 Volt)(16 x 10-6 Farad) = 160 x 10-6 Coulomb

Q = 160 microCoulomb = 160 μC

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