What is the equivalent capacitance of the group of capacitors between points A a

Question

What is the equivalent capacitance of the group of capacitors between points A and B?

Now suppose that a 12 V battery is connected across A and B, and the capacitors are fully charged.

How much (total) energy is stored in this group of capacitors?

Find the value of Q (magnitude of charge on one plate) for the 15 microF capacitor.

Find the value of Q for the 8.2 microF capacitor.

Find the value of Q for the 22 microF capacitor.

What is the value of Qtot (total charge stored) for the entire group of capacitors?

What is the equivalent capacitance of the group of capacitors between points A and B? Now suppose that a 12 V battery is connected across A and B, and the capacitors are fully charged. How much (total) energy is stored in this group of capacitors? Find the value of Q (magnitude of charge on one plate) for the 15 microF capacitor. Find the value of Q for the 8.2 microF capacitor. Find the value of Q for the 22 microF capacitor. What is the value of Qtot (total charge stored) for the entire group of capacitors?

Explanation / Answer

a)

8.2 uF and 22 uF are in series

1/C' =1/8.2 +1/22

C' =5.97 uF

5.97 uF and 15 uF are in parllel ,so equivalent resistance

Ceq=15+5.97 =20.97 uF

b)

Total Energystored

E=(1/2)CeqV2=(1/2)*(20.97*10-6)*122

E=1.51*10-3 J or 1.51 mJ

c)

Charge on 15 uC is

Q15=CV =(15*10-6)*12

Q15=1.8*10-4 C or 180 uC

d)

Total Charge

Q=CeqV=(20.97*10-6)*12=2.52*10-4 C

Charge on 8.2uF

Q8.2=Q-Q15=2.52*10-4-1.8*10-4

Q8.2=7.2*10-5 C or 71.68 uC

e)

charge on 22 uF is

Q22=Q8.2=7.2*10-5 C or 71.68 uC

f)

Total Charge

Qtotal=2.52*10-4 C or 251.7 uC

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