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Registered Member #4659
Joined: Sun Apr 29 2012, 06:14PM
Location:
Posts: 158
Tony Matt wrote ...
C = 8.854 * K * A * (N-1) / D
C = CAPACITANCE IN pF
K = DIELECTRIC CONSTANT
N = NUMBER OF PLATES
A = PLATE AREA [ SQUARE METER ]
D = DIELECTRIC THICHNESS [METER]
IF THE TW0 PLATES ARE COILED AS YOU SHOW IN THE BEGIN, THE TOTAL CAPACITANCE IS SHALL BE TWICED...
Based on this data, I wrote a Python computer program to calculate the total energy that could be stored in a homemade capacitor based on these values. Is my math right?
#!/usr/bin/python3
K = float(eval(str(input("Dielectric Constant? ") )))
A = float(eval(str(input("Plate area (Square meters)? "))))
D = float(eval(str(input("Dielectric thickness (meters)? "))))
n = 2 #two plates on a regular capacitor
nminusone = n-1
picofarads = (8.854*K*A*nminusone)/D
picofarads = picofarads*2 # rolled capacitor
farads = picofarads*(10**-12)
print(str(picofarads/1000) + " uF capacitor")
S = float(eval(str(input("Dielectric strength (V/m) ? "))))
maxvoltage = S*D
print("Maximum voltage: " + str(maxvoltage) + "V")
J=farads*maxvoltage*maxvoltage
print("Stored Energy: " + str(J) + "J")
I looked up values for wax paper and found Di.Constant=~3, Di.Strength = 3.6E7 V/m. This program tells me I could store upwards of 10KJ in a capacitor made from two rolls of allumninum foil and two rolls of wax paper. Is that right?
EDIT: there was a bug in the code. I fixed it above and it gives sane results now.
Registered Member #3343
Joined: Thu Oct 21 2010, 04:06PM
Location: Toronto
Posts: 311
Yanom: 1 - The info from Tony is the practical and acceptable formula to start a capacitor design. 2- We are skiping the capacitor design procedure and going to abstracts ... 3- There several points that may be not true, or need to be clarified (in the program and in the conclusions).
In order to get a result, lets leave the program at side and try calculate step by step:
info acceptable: C = 8.854 * K * A * (N-1) / D C = CAPACITANCE IN pF K = DIELECTRIC CONSTANT (use 3.00 as you wrote) N = NUMBER OF PLATES (use two, rolled, ayw ) D = DIELECTRIC THICKNESS [ METER ] ( to be calculated ) A = PLATE AREA [ SQUARE METER ] ( to be calculated ) assume that the waxed paper dielectric is 20kV/mm assume that a rolled cap has twice the capacitance of flat cap of same area
Problem: Calculate a rolled capacitor, 10 microfarads, 1000 maximum peak voltage. a - State the thickness of the available foil. State the thickness of the available paper. b - first calculate the dielectric thickness. b - calculate the aluminum foil area and dimensions of each foil. c - calculate paper area and dimension of each paper sheet. d - calculate the energy and the energy per sq cm.
I hope you following the above steps it will be easier for us review and providing a oppinion.
Registered Member #3700
Joined: Sat Feb 19 2011, 12:59PM
Location:
Posts: 107
Hi !
I did some calculations, let me know if Im in the right track
a - Thickness of aluminum foil = 0.018mm (Jerrolds Wrap kitchen foil)... Also assuming that the available waxed paper thickness as 0.1mm.
b- calculating the required paper thickness:
A safety factor on the capacitor voltage will be good practice. Lets use SF as 1.5, So the cap design voltage will be 1500Vpk.
1- assuming that are some small air bubbles 0.1mm thick inside the dielectric, and the bubble air ionizing gradient as 9000/mm. (corona starting voltage)
2- L2=(E/G1-L1)*(K2/K1)
were L2= paper thicness E= applied pk voltage on the cap = 1500V G1 = air max gradient starting ionizing L1= air bubble thickness = 0.1mm K1= air buble dielectric constant =1 K2 = paper dielectric constant = 3
L2=(1500/9000 - 0.1) * (3/1) = 0.2mm
The minimal paper thickness to be 0.2mm.
Lets use 2 sheet of paper, total dielectric thickness as 0.2mm.
Area of one aluminum electrode (flat electrodes): C = 8.854 * K * A * (N-1) / D A = C*D /[ 8.854 *K*(n-1)] A = 10000000 * 0.0002 / [8.854 *3*(2-1)] A = 75.3m2 But the cap has coiled electrodes, so each electrode foil to be 37.65 square meter .
Assuming the foil wide as 300mm, and usefull wide as 280mm, each capacitor plate dimension will be 0.28m x 134m.
The waxed paper dielectric shall have similar dimensions.
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