Three capacitors are connected as shown in the figure below to a constant potent

Question

Three capacitors are connected as shown in the figure below to a constant potential difference of 6 V. The gaps between the plates of all three capacitors are filled with air with dielectric constant k = 1.0. giving the capacitance values C_1 = 2 mu F, C_2 = 3 and C_3 = 4 mu F What is the magnitude of the charge Q_2 on each of the plates of capacitor C_2? a) 22.3 mu C b) 10.3 mu C c) 12.0 mu C d) 18.0 mu C d) 18.0 mu C e) 3.71 mu C What is the total energy U_tot stored on the three capacitors? a) U_tot = 22.2 mu J b) U_tot = 33.7 mu J c) U_tot = 44.5 mu J d) U_tot = 55.3 mu J e) U_tot = 66.9 mu J A dielectric material with k = 5.4 is now inserted between the plates of capacitor C_1 What is the change in the amount of energy stored on this capacitor? a) |delta U_1| = 76.4 mu J b) |delta U_1| = 158 mu J c) |delta U_1| = 267 mu J d) |delta U_1| = 378 mu J e) |delta U_1| = 480 mu J

Explanation / Answer

c2 and c3 are in series c23 = c2c3/c2+c3 = 3*4/7 = 1.71*10^-6 F

c1 and c23 are in paralle

so voltage is same

v1 = v23 = 6

q23 = c23*v = 10.28*10^-6 C

in seriws q is same

q2 = q3 = q23 = 10.28*10^-6 C

ctot = c1+c23 = 3.71*106-6 F

u tot = 1/2cv^2 = 66.78*106-6 J

c1' = kc1 = 5.4*2 = 10.8*10^-6 F

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