One thing to remember is that a high voltage capacitor isn't usually the biggest inductance or resistance in the circuit. A 4000v 500nf (4j) capacitor
(two microwave caps in series) connected to a load through 5m of RG-6 cable, (1.5 uH, .25 ish ohm dc resistance) will momentarily deliver only 4.5kA,
reaching a peak about 1.35 microseconds after it is connected. The resistance of the line is about .25 ohm, while it's inductive reactance is about
1.74 ohm.
The resistance and inductance of the capacitor itself is probably smaller than that of even a larger capacitance lower voltage electrolytic
cacapacitor The whole system will recharge that capacitor in the opposite direction and go through several cycles like this at a frequency of 184khz
before it runs out of energy, and the fraction of energy dissipated in the load, cable, and capacitor will depend on what the resistance of each is.
Now, if we model a 200v 5000uF (100j) capacitor, and the same line, we get a peak current of about 800 amps, at about 135 microseconds after
connection. The cable resistance is still .25 ohms, and the inductance reactance is .0174 ohms. In both cases, I'm assuming the bridgewire and
capacitor resistance are small compared to cable resistance, although this may not be the case with the electrolytic capacitors. Because the
resistance dominates, we don't get an oscillation this time, which is a good thing in this case since that would destroy an electrolytic capacitor.
The funny thing is that in both cases , the ratio of how much heat dissipates in one part vs another depends just on the ratio of resistances between
the two parts, not on the peak current. It's worth noting that for the same bridge wire, the initial rate of heating is about 30 times higher with the
high voltage low energy capacitor.
But we can do better. Because the main thing limiting current to 4.5 kA is the massive inductance of the cable, we can add higher resistance
bridgewires and get a higher efficiency of heat transfer that way, without reducing the peak current or rise time by that much. If we include a 1 ohm
bridge wire in the circuit, the high voltage circuit is still delivering 1.87 kA and 3500kW peak power at the load, whereas the low voltage circuit
would only deliver a peak current of 160 A and a peak power of 25.6 kW to the same load. High voltage doesn't mean you can pass a given current
through a wire with less heating. It just means you can pass the same power through with less current. But, if you connect a 1 ohm load to both, the
current and voltage going into the load will be much higher and that will lead to a much higher peak power for the high voltage setup.
Oh, one more thing: those microwave capacitors should be able to hold 4kv by themselves. You could probably make a 2uf 4kv discharge without hurting those
capacitors.. the only problem with charging them in parallel to 4kv (well, besides the risk of damaging them) is that you now have a very lethal
capacitor bank that has enough voltage to arc through wiring insulation or a switch handle and cause electrocution.
[Edited on 9-1-2021 by Vomaturge] |
