(35 points) Three capacitors are connected as shown in the figure below. The gap
ID: 1771625 • Letter: #
Question
(35 points) Three capacitors are connected as shown in the figure below. The gaps between the p capacitors are filled with air (K 1.0), giving the capacitance values listed in the figure. A constant pote 6 V is maintained between points A and B on the circuit. lates of all three 19 C2 6 V Cs (10 points) When al hre capacitrs are fully harged, what isthe magntude of the charge and the voltage on each capacitor? a23+4 6.002a 12.00 Vi- (10 points) what is the effective capacitance of the system? Eq (10 points) when all three capacitors are fully charged, what is the total energy stored in all three capacitors? allowed to fully charge. How does the energy stored on this capacitor change? 6 the energy increases b. the energy stays the same c. the energy decreases (5 points) A dielectric material with x-5.0 is now inserted between the plates of capacitor C, and the capacitorsExplanation / Answer
Q = C*V
C3 and C4 are in series hence,
1/C34 = 1/C3 + 1/C4
1/C34 = 1/3 + 1/4
C34 = 12/7
C2 and C34 are in parallel hence,
Cnet = C34 + C2 = 12/7 + 2 = 26/7 MuF
A)
Q2 = (2*10^-6)*6 = 1.2*10^-5 A
Q34 = (12/7*10^-6)*6 = 10.29*10^-6 A
Q3 = Q4 = Q34 = 10.29*10^-6 A
B)
Cnet = 26/7 MuF
C)
Energy = 1/2C*V^2
E2 = (1/2)*(2*10^-6)*6^2 = 36*10^-6
V3 = (10.29*10^-6)/(3*10^-6) = 10.29/3 = 3.43 V
V4 = (10.29*10^-6)/(4*10^-6) = 10.29/4 = 2.5725 V
E3 = (1/2)*(3*10^-6)*3.43^2 = 17.64*10^-6
E4 = (1/2)*(4*10^-6)*3.43^2 = 25.53*10^-6
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