Question

A capacitor made from a stack of 6 metal plates separated by thin layers of plastic. The plastic is 0.2mm thick. The copper plates are 1mm thick. Each component is a square with 10cm sides. Plastic has a relative dielectric constant of 2.4 and copper has a resistivity of 1.7e-8 ohm-meters and this capacitor is charged to a 1V potential..a) Determine the effective capacitance of this capacitor. b) Determine the electric field at the center of this multilayer capacitor in the middle of the center plastic sheet

Answer 1

given
Area of each plate, A = L^2
= 0.1^2
= 0.01 m^2
distance between the plates, d = 0.2 mm = 0.2*10^-3 m

dielctric constant, k = 2.4

using 6 plates 5 capacitors can be made.

and these 5 capacitors are in series.

Capacitance of each capacitor, C = k*A*epsilon/d

= 2.4*0.01*8.854*10^-12/(0.2*10^-3)

= 1.06*10^-9 F

let C_eff is the effective capacitance,

1/C_eff = 1/C + 1/C + 1/C + 1/C + 1/C

C_eff = C/5

= 1.06*10^-9/5

= 2.12*10^-10 F (Answer)

b) potential difference aross each capacitor, V = 1/5

= 0.2 V

electric field between center capacitor,

E = (V/d)/k

= (0.2/(0.2*10^-3))/2.4

= 417 N/c (Answer)