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kenw232

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I'm trying to cross check mathematically the mA being discharged from a .33uF capacitor which is charged to about 1200V by a circuit (see single_circuit.jpg) which is provided 37W of power to it. I do it three ways.

1) The circuit draws 35W total. 13V @ 5A = 65W. But the power supply drops the 13V to 7V to maintain the 5A so the effective wattage is 7V x 5A = 35W. I just assumed this 35W carries through the entire circuit and out T2 because energy cannot be created and destroyed and there is little to no resistance from what I can see. So the wattage coming out of the capacitor is still roughly < 35W. We should use Vavg I think, not Vpeak, so 35W / 600Vavg = 58mA.

2) Now (1) makes sense, but I was hoping there was a cross check. I noticed on a page like this:

http://cnx.org/content/m42427/latest/?collection=col11406/latest (see Example 2)

you can calculate the mA from a capacitor via it's reactance. X = 1 / (2 x Pi x freq x C). As shown there I do the same. I put the gas discharge tube on the scope and get the attachment single_circuit_scope.jpg.

X = 1 / (2 x Pi x freq x C)

X = 1 / (6.28318 x 42 x 0.00000033)

X = 11483 Ohms

720Vrms / 11483 = 0.06270A or 62mA

Great, this works. Essentially the same as (1). So (1) and (2) validate each other. This also means the wattage then is 720Vrms x .0627 = 45W. 45W is a little too high and not valid I think. After all Vrms is for AC, I have changing DC. So if we used Vavg its 600/11483 = 52mA, 52mA x 600Vavg = 31W. This makes more sense and probably also accounts for the wattage loss from stepping up the voltage @ T1. (35W - 31W = 4W loss).

3) But then I found E = (V² x C) / 2 which is used to calculate the energy per pulse from a capacitor discharge. Also conveniently calculated at:

http://www.vishay.com/resistors/pulse-energy-calculator/

E = (1200Vpeak² x 0.00000033) / 2

E = .2376 Joules per pulse

Joules per second = .2376 x frequency

Joules per second = .2376 x 42.4Hz

Joules per second = 10.07.

Joules per second is the same as watts.

Watts = 10W. This is shown easily and proven with the Vishay pulse calculator at that URL above. Or just see the attachment calc2.jpg. 10W? Why the sudden massive drop in wattage?

So this is where I am right now, I want to know why (3) is only giving me 10W. How can 1 and 2 work out, but 3 be so far off. Is (3) not an applicable formula to use in this case?

Any help in clarifying what I am doing wrong would be appreciated.

1) The circuit draws 35W total. 13V @ 5A = 65W. But the power supply drops the 13V to 7V to maintain the 5A so the effective wattage is 7V x 5A = 35W. I just assumed this 35W carries through the entire circuit and out T2 because energy cannot be created and destroyed and there is little to no resistance from what I can see. So the wattage coming out of the capacitor is still roughly < 35W. We should use Vavg I think, not Vpeak, so 35W / 600Vavg = 58mA.

2) Now (1) makes sense, but I was hoping there was a cross check. I noticed on a page like this:

http://cnx.org/content/m42427/latest/?collection=col11406/latest (see Example 2)

you can calculate the mA from a capacitor via it's reactance. X = 1 / (2 x Pi x freq x C). As shown there I do the same. I put the gas discharge tube on the scope and get the attachment single_circuit_scope.jpg.

X = 1 / (2 x Pi x freq x C)

X = 1 / (6.28318 x 42 x 0.00000033)

X = 11483 Ohms

720Vrms / 11483 = 0.06270A or 62mA

Great, this works. Essentially the same as (1). So (1) and (2) validate each other. This also means the wattage then is 720Vrms x .0627 = 45W. 45W is a little too high and not valid I think. After all Vrms is for AC, I have changing DC. So if we used Vavg its 600/11483 = 52mA, 52mA x 600Vavg = 31W. This makes more sense and probably also accounts for the wattage loss from stepping up the voltage @ T1. (35W - 31W = 4W loss).

3) But then I found E = (V² x C) / 2 which is used to calculate the energy per pulse from a capacitor discharge. Also conveniently calculated at:

http://www.vishay.com/resistors/pulse-energy-calculator/

E = (1200Vpeak² x 0.00000033) / 2

E = .2376 Joules per pulse

Joules per second = .2376 x frequency

Joules per second = .2376 x 42.4Hz

Joules per second = 10.07.

Joules per second is the same as watts.

Watts = 10W. This is shown easily and proven with the Vishay pulse calculator at that URL above. Or just see the attachment calc2.jpg. 10W? Why the sudden massive drop in wattage?

So this is where I am right now, I want to know why (3) is only giving me 10W. How can 1 and 2 work out, but 3 be so far off. Is (3) not an applicable formula to use in this case?

Any help in clarifying what I am doing wrong would be appreciated.