Question

Question 13 This question contains multiple parts. Make sure to read all the instructions and answer each part Consider a round parallel plate capacitor consisting of two circular metal plates of radius, R-1.0 cm, separated by d = 150 μm of air. The capacitor is connected to a potential source, as shown in the figure below. Part a Calculate the capacitance of this capacitor in picoFarads? (1pF 10-12 F)

Answer 1

Capacitance of a capacitor C = k epsilon_0 A/d dielectric constant of air = k = l A is the are of circular plate A = pi r^2 = 0.0003142 m^2 and plate separation = 150 mu m epsilon_0 = 8.854 times 10^-12 C^2 /N m^2 substituting all the know values gives C = 183.4 pF potential source = V_0 = 197V we plug the values in band while using the relation give us energy stored in capacitor = U = 1/2 CV^2 = 3.598e - 006 J U = 3598 nJ if the radius is decreased by half and the new radius = r prime = r/2 new area of cross section = A prime = pi r^2 prime = pi r^2/4 = A/4 and new separation between plates = d prime = d/2 new capacitance of capacitor = C prime = k epsilon_0 A prime/d prime = C/2 and the new energy = U prime = 1/2 C prime v^2