Question

Two capacitors give an equivalent capacitance of 9.70 pF when connected in parallel and an equivalent capacitance of 1.64 pF when connected in series. What is the capacitance of each capacitor? Small capacitor? Big capacitor?

Answer 1

let C1 and C2 are two capacitors

in parallel combination

Equivalent capacitance is Ceq = C1+C2 = 9.7*10^-12

in series

Ceq = C1*C2/(C1+C2) = 1.64*10^-12

then

C1*C2/(9.7*10^-12) = 1.64*10^-12

C1*C2 = 9.7*1.64*10^-24 = 15.9*10^-24 F

(C1-C2)^2 = (C1+C2)^2 - 4C1*C2

(C1-C2)^2 = (9.7*10^-12)^2 - (4*15.9*10^-24) = 30.49*10^-24 F

C1-C2 = 5.52*10^-12...(1)

C1+C2 = 9.7*10^-12...(2)

adding (1) and (2) we get

2*C1 = 15.22*10^-12

C1 = 7.61*10^-12 F = 7.61 pF...is Big capacitor

C2 = (9.7-7.61)*10^-12 = 2.09*10^-12 F = 2.09 pF...is small Capacitor