Three air filled capacitors with circular plates are connected in series. Capaci

Question

Three air filled capacitors with circular plates are connected in series. Capacitor C_1 has a plate diameter of 15.0 cm and plate separation of 0.55 mm, C_2 has a plate diameter of 12.5 cm and a plate separation of 0.49 mm and C_3 has plate diameter of 8.0 cm and plate separation of 0.70 mm. A fourth capacitor C_4 is added in parallel to the three in series, What is the capacitance of C_4 such that the C_eq of all four is one half of the ssmallest capacitance of the three in series? What is the charge on each capacitor?

Explanation / Answer

r1 = 15/2 = 7.5 cm

C1 = eo*A1/d1 = 8.84*10^-12*pi*0.075^2/(0.55*10^-3) = 2.84*10^-10 F

r2 = 12.5/2 = 6.25 cm    d2 = 0.49 mm

C2 = eo*A2/d2 = 8.84*10^-12*pi*0.0625^2/(0.49*10^-3) = 2.21*10^-10 F

r3 = 8/2 = 4 cm    d3 = 0.7 mm

C3 = eo*A3/d3 = 8.84*10^-12*pi*0.04^2/(0.7*10^-3) = 63.5*10^-10 F

1/C123 = 1/C1 + 1/C2 = 1/C3

C123 = 1.22*10^-10 F

C123 & C4 are in parallel

Ceq = C123 + C4

Ceq = C2/2

1.22*10^-10 + C4 = 2.21*10^-10

C4 = 99*10^-10 F

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