Question

A multi-layer capacitor is 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.. [6] a) Determine the effective capacitance of this capacitor. [4] b) Determine the electric field at the center of this multilayer capacitor in the middle of the center plastic sheet. _________________________

Answer 1

Area of each plate, A = L^2
= 0.1^2
= 0.01 m^2
d = 0.2 mm = 0.2*10^-3 m
dielctric constant, k = 2.4

here 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

effective capacitance, 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 caoacitor,

E = (V/d)/k

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

= 417 N/c <<<<<<<<<<-----------------Answer