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

Question

You have three parallel plate capacitors, each consisting of two parallel 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 = 15.3 mm, d = 5.10 um, filled with air. Capacitor 2 (C2): r = 13.3 mm, d = 39.9 um, filled with diamond. Capacitor 3 (C3): r = 7.84 mm, d = 14.7 um, filled with Indium Antimonide (InSb).

Material K Value

Air 1.00

Paper 3.50

Glass 4.50

Diamond 5.50

Porcelain 7.00

GaAs 13.2

Ge 16.0

LnSb 17.1

Rank their capacitance from highest to lowest.

Explanation / Answer

For Capacitor 1

For air K=1 from table

C1=KeoA/d =1*(8.85*10-12)*(pi*(15.3*10-3)2)/(5.1*10-6)

C1=1.276*10-9F

For Capacitor C2

K=5.5

C2=5.5*(8.85*10-12)*(pi*(13.3*10-3)2)/(39.9*10-6)

C2=0.678*10-9F

For Capacitor C3 is

K=17.1

C3=17.1*(8.85*10-12)*(pi*(7.84*10-3)2)/(14.7*10-6)

C3=1.988*10-9F

so Ranking

C3>C1>C2

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