# Re: Help with this equation!

```Subject:     Re: Help with this equation!
Date:  Sat, 31 May 1997 13:43:53 -0700
To:  Tesla List <tesla-at-pupman-dot-com>
References:
1

Tesla List wrote:
>
> Subject:      Help with this equation!
>        Date:  Mon, 26 May 1997 21:37:07 -0400
>        From:  Tom Heiber <theiber-at-lonet.ca>
> Organization: Power Surge
>          To:  tesla-at-pupman-dot-com
>
> This is an equation I got from Bert Pool's file.
>
>
>
=======================================================================
>     EQUATION 10: CAPACITANCE OF A TOROID
>                                                     ___________________
>                                                    /    2
>          C =(1+ (0.2781 - d2/d1)) x  2.8  x      /  2 pi  (d1-d2)(d2/2)
>                                                /   -------------------
>                                             \/      4 pi
>
>      C = capacitance in picofarads (+- 5% )
>     d1 = outside diameter of toroid in inches
>     d2 = diameter of cross section (cord) of toroid in inches
>
>     Equation courtesy of Bert Pool
>
>
=======================================================================
>
> CAN ANYONE help me solve for D1 as in D1=........
> I have been trying to do this without any results (I suck at math)
>
> Thank You
>
> Tom Heiber

Tom
I like to make look up tables with a spread sheet for problems
like this. I will include the table I made last year using this same
equation you have above you might find it useful.

The table was too wide so I had to divide it into. The first
section is the left half and the second section is the right half.

[section 1 of table 1]

To use this table choose a dia for (d2) across the top of the table
from 1"-12". Then looking down the left side choose a dia for (d1)
from 6"-60". then look to the intersection of this row and column to
find the calculated (pf) a toroid with those diminsions.

1    2    3    4    5    6    7    8    9   10   11   12
6  6.2  6.6  5.8  4.3  2.5    na   na   na   na   na   na   na
7  6.9  7.8  7.3  6.1  4.4  2.6    na   na   na   na   na   na
8  7.6  8.8  8.7  7.7  6.3  4.5  2.6    na   na   na   na   na
9  8.2  9.8  9.9  9.3  8.0  6.4  4.6  2.7    na   na   na   na
10  8.8  10.7 11.1 10.7 9.7  8.2  6.6  4.7  2.8    na   na   na
11  9.3  11.5 12.2 12.0 11.2 10.0 8.4  6.7  4.8  2.9    na   na
12  9.8  12.3 13.3 13.3 12.6 11.6 10.2 8.6  6.8  4.9  3.0    na
13  10.3 13.1 14.2 14.4 14.0 13.1 11.9 10.4 8.7  6.9  5.0  3.1
14  10.8 13.8 15.2 15.6 15.3 14.6 13.5 12.1 10.6 8.8  7.0  5.1
15  11.2 14.5 16.1 16.6 16.6 16.0 15.1 13.8 12.4 10.7 9.0  7.1
16  11.7 15.1 16.9 17.7 17.8 17.4 16.6 15.4 14.1 12.6 10.9 9.1
17  12.1 15.8 17.7 18.7 18.9 18.7 18.0 17.0 15.8 14.3 12.7 11.0
18  12.5 16.4 18.5 19.6 20.0 19.9 19.4 18.5 17.4 16.0 14.5 12.9
19  12.9 17.0 19.3 20.5 21.1 21.1 20.7 20.0 18.9 17.7 16.3 14.7
20  13.3 17.5 20.0 21.4 22.1 22.2 22.0 21.3 20.4 19.3 18.0 16.5
21  13.7 18.1 20.7 22.3 23.1 23.4 23.2 22.7 21.9 20.9 19.6 18.2
22  14.0 18.6 21.4 23.1 24.0 24.4 24.4 24.0 23.3 22.4 21.2 19.9
23  14.4 19.2 22.1 23.9 25.0 25.5 25.6 25.3 24.7 23.9 22.8 21.6
24  14.7 19.7 22.7 24.7 25.9 26.5 26.7 26.5 26.0 25.3 24.3 23.2
25  15.1 20.2 23.3 25.4 26.8 27.5 27.8 27.7 27.3 26.7 25.8 24.7
26  15.4 20.7 24.0 26.2 27.6 28.5 28.9 28.9 28.6 28.0 27.3 26.3
27  15.7 21.1 24.6 26.9 28.4 29.4 29.9 30.0 29.8 29.4 28.7 27.8
28  16.0 21.6 25.2 27.6 29.3 30.3 30.9 31.1 31.0 30.7 30.0 29.2
29  16.3 22.0 25.7 28.3 30.1 31.2 31.9 32.2 32.2 31.9 31.4 30.6
30  16.6 22.5 26.3 29.0 30.8 32.1 32.9 33.3 33.4 33.2 32.7 32.0
31  16.9 22.9 26.9 29.6 31.6 33.0 33.8 34.3 34.5 34.4 34.0 33.4
32  17.2 23.4 27.4 30.3 32.3 33.8 34.8 35.3 35.6 35.5 35.2 34.7
33  17.5 23.8 27.9 30.9 33.1 34.6 35.7 36.3 36.7 36.7 36.5 36.0
34  17.8 24.2 28.5 31.5 33.8 35.4 36.6 37.3 37.7 37.8 37.7 37.3
35  18.1 24.6 29.0 32.2 34.5 36.2 37.5 38.3 38.8 38.9 38.9 38.6
36  18.4 25.0 29.5 32.8 35.2 37.0 38.3 39.2 39.8 40.0 40.0 39.8
37  18.6 25.4 30.0 33.4 35.9 37.8 39.2 40.1 40.8 41.1 41.2 41.0
38  18.9 25.8 30.5 33.9 36.5 38.5 40.0 41.0 41.7 42.1 42.3 42.2
39  19.2 26.2 31.0 34.5 37.2 39.3 40.8 41.9 42.7 43.2 43.4 43.3
40  19.4 26.6 31.5 35.1 37.9 40.0 41.6 42.8 43.6 44.2 44.5 44.5
41  19.7 26.9 31.9 35.6 38.5 40.7 42.4 43.7 44.6 45.2 45.5 45.6
42  19.9 27.3 32.4 36.2 39.1 41.4 43.2 44.5 45.5 46.2 46.6 46.7
43  20.2 27.7 32.8 36.7 39.7 42.1 43.9 45.3 46.4 47.1 47.6 47.8
44  20.4 28.0 33.3 37.3 40.4 42.8 44.7 46.2 47.3 48.1 48.6 48.9
45  20.7 28.4 33.7 37.8 41.0 43.5 45.4 47.0 48.2 49.0 49.6 49.9
46  20.9 28.7 34.2 38.3 41.5 44.1 46.2 47.8 49.0 49.9 50.6 51.0
47  21.2 29.1 34.6 38.8 42.1 44.8 46.9 48.6 49.9 50.8 51.6 52.0
48  21.4 29.4 35.0 39.3 42.7 45.4 47.6 49.3 50.7 51.7 52.5 53.0
49  21.6 29.8 35.5 39.8 43.3 46.1 48.3 50.1 51.5 52.6 53.5 54.0
50  21.9 30.1 35.9 40.3 43.9 46.7 49.0 50.9 52.3 53.5 54.4 55.0
51  22.1 30.4 36.3 40.8 44.4 47.3 49.7 51.6 53.1 54.4 55.3 56.0
52  22.3 30.8 36.7 41.3 45.0 47.9 50.4 52.3 53.9 55.2 56.2 56.9
53  22.5 31.1 37.1 41.8 45.5 48.5 51.0 53.1 54.7 56.1 57.1 57.9
54  22.8 31.4 37.5 42.3 46.0 49.1 51.7 53.8 55.5 56.9 58.0 58.8
55  23.0 31.7 37.9 42.7 46.6 49.7 52.3 54.5 56.3 57.7 58.9 59.7
56  23.2 32.0 38.3 43.2 47.1 50.3 53.0 55.2 57.0 58.5 59.7 60.7
57  23.4 32.4 38.7 43.6 47.6 50.9 53.6 55.9 57.8 59.3 60.6 61.6
58  23.6 32.7 39.1 44.1 48.1 51.5 54.3 56.6 58.5 60.1 61.4 62.5
59  23.8 33.0 39.5 44.5 48.7 52.1 54.9 57.3 59.2 60.9 62.2 63.3
60  24.0 33.3 39.9 45.0 49.2 52.6 55.5 57.9 60.0 61.7 63.1 64.2

[section2 table 1]

Use this section same as above. It covers (d2's) from 13"-24"
with the same range of (d1's).

13   14   15   16   17   18   19   20   21   22   23   24
6    na   na   na   na   na   na   na   na   na   na   na   na
7    na   na   na   na   na   na   na   na   na   na   na   na
8    na   na   na   na   na   na   na   na   na   na   na   na
9    na   na   na   na   na   na   na   na   na   na   na   na
10    na   na   na   na   na   na   na   na   na   na   na   na
11    na   na   na   na   na   na   na   na   na   na   na   na
12    na   na   na   na   na   na   na   na   na   na   na   na
13    na   na   na   na   na   na   na   na   na   na   na   na
14  10.8   na   na   na   na   na   na   na   na   na   na   na
15  11.2 14.5   na   na   na   na   na   na   na   na   na   na
16  11.7 15.1 16.9   na   na   na   na   na   na   na   na   na
17  12.1 15.8 17.7 18.7   na   na   na   na   na   na   na   na
18  12.5 16.4 18.5 19.6 20.0   na   na   na   na   na   na   na
19  12.9 17.0 19.3 20.5 21.1 21.1   na   na   na   na   na   na
20  13.3 17.5 20.0 21.4 22.1 22.2 22.0   na   na   na   na   na
21  13.7 18.1 20.7 22.3 23.1 23.4 23.2 22.7   na   na   na   na
22  14.0 18.6 21.4 23.1 24.0 24.4 24.4 24.0 23.3   na   na   na
23  14.4 19.2 22.1 23.9 25.0 25.5 25.6 25.3 24.7 23.9   na   na
24  14.7 19.7 22.7 24.7 25.9 26.5 26.7 26.5 26.0 25.3 24.3   na
25  15.1 20.2 23.3 25.4 26.8 27.5 27.8 27.7 27.3 26.7 25.8 24.7
26  15.4 20.7 24.0 26.2 27.6 28.5 28.9 28.9 28.6 28.0 27.3 26.3
27  15.7 21.1 24.6 26.9 28.4 29.4 29.9 30.0 29.8 29.4 28.7 27.8
28  16.0 21.6 25.2 27.6 29.3 30.3 30.9 31.1 31.0 30.7 30.0 29.2
29  16.3 22.0 25.7 28.3 30.1 31.2 31.9 32.2 32.2 31.9 31.4 30.6
30  16.6 22.5 26.3 29.0 30.8 32.1 32.9 33.3 33.4 33.2 32.7 32.0
31  16.9 22.9 26.9 29.6 31.6 33.0 33.8 34.3 34.5 34.4 34.0 33.4
32  17.2 23.4 27.4 30.3 32.3 33.8 34.8 35.3 35.6 35.5 35.2 34.7
33  17.5 23.8 27.9 30.9 33.1 34.6 35.7 36.3 36.7 36.7 36.5 36.0
34  17.8 24.2 28.5 31.5 33.8 35.4 36.6 37.3 37.7 37.8 37.7 37.3
35  18.1 24.6 29.0 32.2 34.5 36.2 37.5 38.3 38.8 38.9 38.9 38.6
36  18.4 25.0 29.5 32.8 35.2 37.0 38.3 39.2 39.8 40.0 40.0 39.8
37  18.6 25.4 30.0 33.4 35.9 37.8 39.2 40.1 40.8 41.1 41.2 41.0
38  18.9 25.8 30.5 33.9 36.5 38.5 40.0 41.0 41.7 42.1 42.3 42.2
39  19.2 26.2 31.0 34.5 37.2 39.3 40.8 41.9 42.7 43.2 43.4 43.3
40  19.4 26.6 31.5 35.1 37.9 40.0 41.6 42.8 43.6 44.2 44.5 44.5
41  19.7 26.9 31.9 35.6 38.5 40.7 42.4 43.7 44.6 45.2 45.5 45.6
42  19.9 27.3 32.4 36.2 39.1 41.4 43.2 44.5 45.5 46.2 46.6 46.7
43  20.2 27.7 32.8 36.7 39.7 42.1 43.9 45.3 46.4 47.1 47.6 47.8
44  20.4 28.0 33.3 37.3 40.4 42.8 44.7 46.2 47.3 48.1 48.6 48.9
45  20.7 28.4 33.7 37.8 41.0 43.5 45.4 47.0 48.2 49.0 49.6 49.9
46  20.9 28.7 34.2 38.3 41.5 44.1 46.2 47.8 49.0 49.9 50.6 51.0
47  21.2 29.1 34.6 38.8 42.1 44.8 46.9 48.6 49.9 50.8 51.6 52.0
48  21.4 29.4 35.0 39.3 42.7 45.4 47.6 49.3 50.7 51.7 52.5 53.0
49  21.6 29.8 35.5 39.8 43.3 46.1 48.3 50.1 51.5 52.6 53.5 54.0
50  21.9 30.1 35.9 40.3 43.9 46.7 49.0 50.9 52.3 53.5 54.4 55.0
51  22.1 30.4 36.3 40.8 44.4 47.3 49.7 51.6 53.1 54.4 55.3 56.0
52  22.3 30.8 36.7 41.3 45.0 47.9 50.4 52.3 53.9 55.2 56.2 56.9
53  22.5 31.1 37.1 41.8 45.5 48.5 51.0 53.1 54.7 56.1 57.1 57.9
54  22.8 31.4 37.5 42.3 46.0 49.1 51.7 53.8 55.5 56.9 58.0 58.8
55  23.0 31.7 37.9 42.7 46.6 49.7 52.3 54.5 56.3 57.7 58.9 59.7
56  23.2 32.0 38.3 43.2 47.1 50.3 53.0 55.2 57.0 58.5 59.7 60.7
57  23.4 32.4 38.7 43.6 47.6 50.9 53.6 55.9 57.8 59.3 60.6 61.6
58  23.6 32.7 39.1 44.1 48.1 51.5 54.3 56.6 58.5 60.1 61.4 62.5
59  23.8 33.0 39.5 44.5 48.7 52.1 54.9 57.3 59.2 60.9 62.2 63.3
60  24.0 33.3 39.9 45.0 49.2 52.6 55.5 57.9 60.0 61.7 63.1 64.2

Rick L. Kirby

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