Question #326648

1. A Cylindrical capacitor having a length of 8 cm is made of two concentric rings with an inner radius as 3 cm and outer radius as 6 cm. Find the capacitance of the capacitor.




2. A parallel-plate capacitor is filled with polystyrene of 0.0002 m thickness. Find the plate area if the new capacitance after the insertion is 3.4 µF.

1
Expert's answer
2022-04-17T17:08:17-0400

1. The capacitance of a cylindrical capacitor is given as follows:


C=2πϵ0Lln(r2/r1)C = \dfrac{2\pi \epsilon_0 L}{\ln(r_2/r_1)}

where L=8cm=0.08mL=8cm = 0.08m, r1=0.03m,r2=0.06mr_1 = 0.03m, r_2 = 0.06m and ϵ08.85×1012F/m\epsilon_0 \approx 8.85\times 10^{-12} F/m is vacuum permittivity. Thus, obtain:


C=2π8.85×10120.08ln(0.06/0.03)6.4×1012FC = \dfrac{2\pi \cdot 8.85\times 10^{-12}\cdot 0.08}{\ln(0.06/0.03)} \approx 6.4\times 10^{-12}F



2. The capacitance of a parallel plate capacitor is:


C=ϵ0ϵAdC=\dfrac{\epsilon_0 \epsilon A}{d}

where AA is the plate area, ϵ=2.55\epsilon =2.55 is the dielectric constant of polystyrene, and d=0.0002md = 0.0002 m is the distance between plates. Expressing AA, get:


A=dCϵ0ϵ=0.0002m3.4×106F8.85×1012F/m2.5530m2A = \dfrac{dC}{\epsilon_0 \epsilon} =\dfrac{0.0002m\cdot 3.4\times10^{-6}F }{8.85\times 10^{-12}F/m\cdot 2.55} \approx 30m^2

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