Question Part Points Submissions Used Three parallel plate capacitors are connec

Question

Question Part Points Submissions Used Three parallel plate capacitors are connected in series. These capacitors have identical geometries. However, they are filled with three different materials. The dielectric constants of these materials are 3.12, 5.38, and 6.80. It is desired to replace this series combination with a single parallel plate capacitor. Assuming that this single capacitor has the same geometry as each of the other three capacitors, determine the dielectric constant of the material with which it is filled.

Explanation / Answer

let c0 be the capacitance of the capaicotr with air

after the dielectric is filled

C1 = k1*c0

C2 = k2*c0

C3 = k3*C0

the equivalent capacitance of C1 , C2 ,C3 = Cs = k4*C0

Cs = k4*C0

In series

1/Cs = 1/C1 + 1/C2 + 1/C3

1/K4 = 1/k1 + 1/k2 + 1/k3

1/k4 = 1/3.12 + 1/5.38 + 1/6.8

k4 = 1.53 <<<========answer

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