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This is probably an obvious question, but if I were to discharge 5 kV from a capacitor bank through a circuit with a resistance of 100 ohms, that capacitor would have to be able to withstand 500 Amps right?

If the discharge pulse was VERY fast (milliseconds) would this make a difference? (Numbers used are completely arbitrary)

Some caps might even produce interesting pyrotechnic effects or go ballistic. Literally. Be sure that the blow-off valve is not obstructed. Capacitors with low ESR (equivalent series resistance) are available for RF and pulse circuits. In your example the cap would be designed and specified for that application. Usually caps have high ESR and self-inductance, and limit the current themselves. Hope this is helpful. mike

ps - for a fast discharge pulse the limit is the inductance of the caps and wiring.

Thank you, that does help. The inductance and capacitance of the circuit determine the frequency of the current.

So it seems like I have to find a way to balance the inductance, capacitance and frequency to get the current I'm looking for.

In an RLC circuit do I use the equivalent impedance , Z=[(R^2)*(XL+XC)]^(1/2), or just the internal resistance of the capacitor.

I'm really only worried about the current the capacitor can take without failure.

Frequency shouldn't come into it, the effect of ESL is to limit the rate of rise of your pulse current.

When a capacitor is charged up it has energy store in it. On discharge this energy is converted to heat in the ESR (equivalent series resistance) of the capacitor and in the discharge resistor. Thus a capacitor with a low ESR compared with the discharge resistance will have little heat generated in it and a lot in the discharge resistance and vice versa.

Got it, so can I use the temperature rating of the capacitor to find out the amount of current it can withstand? I think it's,

Heat = (I^2)R*time (Units of heat being Joules then I convert it to degrees Celsius).

So even though the peak current through the circuit is the same on each component, I mostly have to worry about the ESR, frequency and temperature rating of the capacitor when considering the maximum amount of current it can pass, does that sound right?

Well, I suppose you could try that but there is a problem in "convert it to degrees Celcius ". This would require knowledge of the weight and specific heat of each component in the makeup of the capacitor which will probably not be available.
Is this question just academic interest or are you up against a real problem? If a real problem perhaps you could describe it. If the capacitor is for power factor correction I would expect a voltage rating, frequency rating and microfarad rating and if you stay within these there should be no problem. Keep in mind though that if the power system has a distorted waveform there will be high frequency harmonics which can overheat the capacitor---I've seen this happen. If it's a general use capacitor in electronic circuitry chances are that the maximum energy storage within the voltage rating is not enough to seriously heat the capacitor on a single discharge. A long string of closely spaced discharges might require some experimentation .

Thank you, I'm an EE student researching magnetic pulse welding for a project. The idea is to very quickly pass a large current through a coil to create a magnetic field that collapses a tube placed inside the coil. The current is produced by discharging a capacitor bank, or single high power capacitor.

In this application the resonance frequency is important but for the most part I have what I think are working parameters. i.e. capacitance, inductance, resistance, voltage rating of capacitor...

But I'm still not certain on determining the max amount of current that can safely be discharged from the capacitor in a certain amount of time. Theoretically my circuit would have a RLC time constant of around 100ms

This is the reverse of common practice - usually we put a resistor in series to limit the current. In this case you are trying to maximise the current and you have to minimise the series resistance and inductance. Then there are two things that interest you: one is the pulse current rating of the capacitor, which comes from the manufacturer, and the other is the average current for repeated pulses (I assume you repeat) which is the 'ripple current', again from the capacitor spec sheet. I see your set-up as being very tight, with beefy conductors, to minimise R and L, and with very big capacitors. Your time-scale is quite relaxed, 100ms is a long time electronically. I assume you switch using a big SCR or similar. Hope this is helpful, mike.