A parallel plate capacitor is made by placing polythene (K=2.3) between sheets of aluminium foil. The area of each sheet is 400 cm2, and the spacing is 0.3 mm. Find the capacitance.
Question
A parallel plate capacitor is made by placing polythene (K=2.3) between sheets of aluminium foil. The area of each sheet is 400 cm2, and the spacing is 0.3 mm. Find the capacitance.
Solution
The formula for the capacitance (C) of a parallel plate capacitor is given by:
C = ε * (A/d) * K
where: ε is the permittivity of free space (8.85 x 10^-12 F/m), A is the area of one of the plates (in m^2), d is the distance between the plates (in m), and K is the relative permittivity (dielectric constant) of the material between the plates.
First, we need to convert the given values to the correct units:
The area A = 400 cm^2 = 400 x 10^-4 m^2 = 0.04 m^2 The distance d = 0.3 mm = 0.3 x 10^-3 m = 0.0003 m
Now we can substitute these values into the formula:
C = (8.85 x 10^-12 F/m) * (0.04 m^2 / 0.0003 m) * 2.3 C = 2.77 x 10^-11 F
So, the capacitance of the capacitor is approximately 2.77 x 10^-11 Farads.
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