Electric charge stored in capacitor – problems and solutions

1. Determine the charge in capacitor C5.

Known :

Capacitor 1 (C1) = 6 F

Capacitor 2 (C2) = 6 F

Capacitor 3 (C3) = 3 F

Capacitor 4 (C4) = 12 F

Capacitor 5 (C5) = 6 F

Voltage (V) = 12 Volt

Wanted : Charge in capacitor (C5)

Solution :

Capacitor

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

1/CA = 1/C2 + 1/C3 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6

CA = 6/3 = 2 Farad

Capacitor C4 and capacitor C5 are connected in series. The equivalent capacitor :

1/CB = 1/C4 + 1/C5 = 1/12 + 1/6 = 1/12 + 2/12 = 3/12

CB = 12/3 = 4 Farad

Capacitor CA and capacitor CB are connected in parallel. The equivalent capacitor :

CC = CA + CB = 2 + 4 = 6 Farad

Capacitor C1 and capacitor CC are connected in series :

1/C = 1/C1 + 1/CC = 1/6 F + 1/6 F = 2/6

C = 6/2 = 3 Farad

Electric charge

Electric charge in capacitor C :

q = V C = (12 Volt)(3 Farad) = 36 Coulomb

Capacitor 1 and capacitor CC are connected in series so that electric charge in capacitor C = electric charge in capacitor C1 = electric charge in capacitor CC = 36 Coulomb.

Capacitance of capacitor CC is 6 Farad and charge in capacitor CC is 36 Coulomb. The voltage of the capacitor CC is : V = q/CC = 36 Coulomb / 6 Farad = 6 Volt

Capacitor CC is the equivalent capacitor for capacitor CA and capacitor CB connected in parallel. Voltage of the capacitor CC (VC) = voltage in capacitor CA (VA) = voltage in capacitor CB (VB) = 6 Volt.

Electric charge in capacitor CB :

qB = VB CB = (6 Volt)(4 Farad) = 24 Coulomb

Capacitor CB is the equivalent capacitor for capacitor C4 and C5 connected in series. Connected in series so that the electric charge in capacitor CB (qB) = the electric charge in capacitor C4 (q4) = the electric charge in capacitor C5 (q5) = 24 Coulomb.

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2. Five identical capacitors with a capacitance of 20 µF are connected in series and parallel, as shown in the figure below, with a source of voltage 6 volts. Determine total energy stored in capacitor C5.

Known :

Capacitor C1 = C2 = C3 = C4 = C5 = 20 µF

Voltage (V) = 6 Volt

Wanted : Electric charge stored in capacitor C5

Solution :

Capacitor

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

1/CA = 1/C1 + 1/C2 = 1/20 + 1/20 = 2/20

CA = 20/2 = 10 µF

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

1/CB = 1/C3 + 1/C4 = 1/20 + 1/20 = 2/20

CB = 20/2 = 10 µF

Capacitor CA and capacitor CB are connected in parallel. The equivalent capacitor :

CC = CA + CB = 10 + 10 = 20 µF

Capacitor CC and capacitor C5 are connected in series :

1/C = 1/CC + 1/C5 = 1/20 + 1/20 = 2/20

C = 20/2 = 10 µF

Electric charge

Electric charge in the equivalent capacitor C :

q = V C = (6 Volt)(10 x 10-6 Farad) = 60 x 10-6 Coulomb = 60 µC

Capacitor CC and capacitor 5 are connected in series so that electric charge in the equivalent capacitor C = electric charge in capacitor CC = electric charge in capacitor C5 = 60 µC.

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3. Five capacitors are connected in series and parallel as shown in figure below. Determine electric charges in capacitor C1 (1 µ = 10-6)

Known :

Capacitor 1 (C1) = capacitor 5 (C5) = 9 µF

Capacitor 2 (C2) = capacitor 3 (C3) = capacitor 4 (C4) = 6 µF

Voltage (V) = 12 Volt

Wanted : Electric charge in capacitor C1

Solution :

Capacitor

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

1/CA = 1/C2 + 1/C3 = 1/6 + 1/6 = 2/6

CA = 6/2 = 3 µF

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

CB = CA + C4 = 3 + 6 = 9 µF

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

1/C = 1/C1 + 1/CB + 1/C5 = 1/9 + 1/9 + 1/9 = 3/9

C = 9/3 = 3 µF = 3 x 10-6 Farad

Electric charge

Electric charge in the equivalent capacitor C :

q = V C = (12 Volt)(3 x 10-6 Farad) = 36 x 10-6 Coulomb = 36 µC

Capacitor C1, capacitor CB and capacitor C5 are connected in series so that electric charge in the equivalent capacitor C = electric charge in capacitor C1 = electric charge in the equivalent capacitor CB = electric charge in capacitor C5 = 36 µC.

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