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

Question

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

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?

c) Refer to the previous problem. Find the value of Q (magnitude of charge on one plate) for the 15 ?F capacitor.

d) Refer to the previous problem. Find the value of Q for the 8.2 ?F capacitor.

e) Refer to the previous problem. Find the value of Q for the 22 ?F capacitor.

f) Refer to the previous problem. What is the value of Qtot (total charge stored) for the entire group of capacitors? Hint-- Recall that "Stored charge" is charge transferred by the battery during the process of charging up the capacitors.

Explanation / Answer

A) 8.2 uF and 22 uF are in series

C1 = (8.2*22)/(8.2+22) = 5.97 uF

C1 and 15 uF are in parallel

hence Cnet = 5.97+22 = 27.97 uF

B) U = 0.5*Cnet*V^2 = 0.5*27.97*10^-6*12^2 = 2.01 mJ

C) Q15/(15*10^-6) = 12...

Q15 = 12*15*10^-6   = 180 uC

D) Q8.2 = Q22 = 12*5.97*10^-6 = 71.64*10^-6 C = 71.64 uC

E) Q22 = 71.64 uC

F) Qtot = 71.64+180   = 251.64 uC

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