What is the proper value of L to use for the capacitor?
To construct a 400 pF capacitor for a science project, you plan to use two metal squares separated by spacers. The thinnest spacers available to you are 0.10 mm thick. What should the side length (L) of the metal squares be to achieve the desired capacitance?
1 Answers
The capacitance of a parallel plate capacitor is given by
C= k e0 A /d
where k is the relative permittivity of the dielectric between the plates , assume air=1
e0 = permittivity of space = 8.854 x 10^ -12
A = area of plates = L^2 for square plates
d = distance between plates = 0.10 x 10 ^ -3 meters
C= capacitance = 400 x 10^ -12 F for problem
rearrange equation to solve for A
A= (C d) / (k e0)
A= ( 400 x 10^ -12) (0.10 x 10^ -3) / (1) (8.854 x 10 -12)
A= 4 x 10^ -14 / 8.854 x 10^ -12 = 4.5 x 10^ -3 m^2
L = sqrt(A) = 67.2 mm
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