We use two circular metal plates of radius 0.27 m and thickness 7.9 mm to build a capacitor. We leave a gap of 3.9 mm between the plates and fill half of the space between the plates with a medium with dielectric constant 10.3 and leave the other half filled with air. What is the capacitance of this capacitor?
Hint: you can treat this problem as two capacitors of area A/2 wired in parallel. One is filled with the dielectric medium, and the other with air. |
r = radius = 0.27 m
A = Area = r2 = 3.14
(0.27)2 = 0.23 m2
d = width = 0.0039 m
capacitance with air is given as
C1 =
A/2d
eq-1
capacitance with dielectric is given as
C2 = k
A/2d
eq-2
total capacitance is given as
C = C1 + C2
C = A/2d +
k
A/2d
C = (k + 1) ( A/2d )
C = (10.3 + 1) (8.85 x 10-12) (0.23) /(2 x 0.0039) = 2.95 x 10-9 F
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