You have three parallel plate capacitors, each consisting of two parallel circul

Question

You have three parallel plate capacitors, each consisting of two parallel circular disks of metal separated by a gap filled with some material. Rank the capacitors by their capacitances from highest to lowest, based on the provided plate radii (r), plate separations (d), and filler materials. Dielectric constants for each material can be found in the table to the right. Capacitor 1 (C1):  r = 15.6 × 10-3 m, d = 5.20 × 10-6 m, filled with air. Capacitor 2 (C2):  r = 13.3 × 10-3 m, d = 39.9 × 10-6 m, filled with diamond. Capacitor 3 (C3):  r = 7.92 × 10-3 m, d = 14.9 × 10-6 m, filled with Indium Antimonide (InSb).

You have three parallel plate capacitors, each consisting of two parallel circular disks of metal separated by a gap filled with some material. Rank the capacitors by their capacitances from highest to lowest, based on the provided plate radii (r), plate separations (d), and filler materials. Dielectric constants for each material can be found in the table to the right. Capacitor 1 (C): r 15.6 x 103 m, d 5.20 x 105 m, filled with air. Capacitor 2 (Ca): r 13.3 x103 m, d 39.9 x106 m, filled with diamond Capacitor 3 (CB): r 7.92 x 103 m, d 14.9 x106 m, filled with Indium Antimonide (Insb). Material K Highest Air 1.00 3.50 Paper 4.50 Glass Diamond 5.50 Porcelain 700 13.2 GaAs 16.0 Ge Lowest 17.7 InSb C2 C1

Explanation / Answer

capacitance=k*epsilon*A/d

where k=dielectric constant

epsilon=8.85*10^(-12)

A=area=pi*r^2

d=distance between the plates

capacitor 1:
capacitance=1*8.85*10^(-12)*pi*(15.6*10^(-3))^2/(5.2*10^(-6))=1.3012*10^(-9) F

capacitor 2:

capacitance=5.5*8.85*10^(-12)*pi*(13.3*10^(-3))^2/(39.9*10^(-6))=6.7793*10^(-10) F

capacitor 3:

capacitance=17.7*8.85*10^(-12)*pi*(7.92*10^(-3))^2/(14.9*10^(-6))=2.0717*10^(-9) F

so ranking them from highest to lowest:

capacitor 3 > capacitor 1> capacitor 2

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