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Re: [TCML] Calculating the C of multiple Spheres for a top load ?



On 26/2/2012 12:56, jeff mill wrote:
Hell again
I’m puzzled . If I plug in an 8” dia sphere in TM it comes up with 11.4pf, If I have four of them 4 X 11.4 =5.6pf I would think.  Now the surface area of four of them when calculating, is equal to a 16” sphere but when I plug a 16” sphere into TM is only doubles and comes up with 22.7pf, not 45.6pf like I would think. Can anyone sheds some light on this ?  Which is correct ?

Thanks JM
The distributed capacitance of an isolated object is proportional to its size, not to its area. The capacitance of four spheres (in a square configuration) is difficult to calculate exactly, but is surely smaller than the capacitance of a toroid enclosing them. A toroid having small diameter of 8" and a large diameter of, say, 24" (0.61 x 0.20 m) has 27.5 pF of capacitance. Four spheres far apart would have 4 x 11.30 = 45.2 pF. (Now I have to find a way to calculate the exact capacitance of four spheres...) A first approximation for the case above results in 11.30 x 2.04383 = 20.0953 pF.
With the spheres touching, 11.30 x 1.69955 = 19.2050 pF.

Antonio Carlos M. de Queiroz



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