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I'm looking for some insight on whether an 1000 Farads at 2.7v or 5.5v would be more effective than say 10,000uF at 400v-450v when creating a strong magnetic coil. The intent is something similar to what I find when examining Coil Gun experiments. Some of the equations I have referenced are :

The amount of potential energy stored in a capacitor depends on the voltage:

            PE = ½ C V^2 
 Where C is capacitance in farads, and V is voltage

And

            v = V * sqrt(C/m) / 10
 Where v is velocity in m/s, V is voltage, C is capacitance in farads, and m is mass in kilograms

I feel like the Cost/Benefit seems like having loads of amps at low voltage would be better than lots of amps at high voltage merely because supercaps pack soo many more Farads. I am given pause because of the v^2 in the energy equation, and the sqrt in the velocity equation.

Additional Information to Consider: Materials cost as of 5/oct/14-

Small Aluminum electrolytic capacitors 450V 1000UF - $1.50 each

SAMWHA super capacitor 2.7V 500F - $5.67 each

Large Electrolytic capacitor 2200uf 450v - $13.20 each

This Last example is what I see in most coilgun examples use and may be more available than the quick search I did for my initial search.

Please also consider the loss of capacitance when run in series vs addition of capacitance when in parallel. As well as the use of the capacitors in other types of experiments if the end result is very similar to each other.

Your thoughts and insights would be appreciated.

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    \$\begingroup\$ See electronics.stackexchange.com/questions/69366/… \$\endgroup\$ – pjc50 Oct 6 '14 at 9:46
  • \$\begingroup\$ at 3-5V you would need thousands of amperes to get useful energy converted into kinetic energy as fast as you need it. pjc50's answer to the one he linked is pretty good. read it! \$\endgroup\$ – KyranF Oct 6 '14 at 9:56
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If we consider only ideal components, then the only number you need to care about is maximum stored energy per unit cost. As you already found, the energy stored in a capacitor is given by

$$ 1/2 \cdot C V^2 $$

The SAMWHA supercapacitor can thus store a maximum of:

$$ 1/2 \cdot 500 \cdot 2.7^2 = 1823 \:\mathrm J $$

The large electrolytic can store up to:

$$ 1/2 \cdot 0.0022 \cdot 450^2 = 222.75 \:\mathrm J $$

In this perspective, only the energy storage matters. That can come from high capacitance or high maximum voltage. It doesn't matter which, because you can shift the balance between current and voltage by changing the design of your coil. A coil with a large number of turns will develop a strong magnetic field without much current. However, it will have a large inductance and will require a high voltage to develop that current quickly. A coil with fewer turns will require more current to develop the same magnetic field, but the inductance will be lower so less voltage is required to get the voltage to rise rapidly.

If you were purchasing ideal capacitors, and you could fabricate an ideal coil, then this would be all you needed to make your decision. However, the real world is not so simple.

Real capacitors have non-ideal effects. It's common to model a capacitor as a network of other components, like this:

schematic

simulate this circuit – Schematic created using CircuitLab

Leakage determines how quickly the capacitor self-discharges. Ideally, this value is infinitely high. It is probably not much of an issue in your application, since you are not storing a charge for a long time.

ESL is the equivalent series inductance. Ideally this value is 0. This inductance places an upper bound on how quickly the current through the capacitor can change. You will want to make sure that the combined ESL of all your capacitors is at least an order of magnitude lower than the inductance of your coil, otherwise you will not get current, and thus the magnetic field, to rise quickly.

ESR is the equivalent series resistance. Ideally this value is 0. Here is the real problem for your application. You will be, at peak, drawing a very high current through your capacitors. This current must also flow through the ESR, and it is subject to all the physical laws of resistance. That includes dropping voltage, according to Ohm's law:

$$ E = IR $$

And converting electrical energy to heat, according to Joule heating:

$$ P = I^2 R $$

Any voltage dropped across ESR is voltage not available to drive your coil. If current is high enough relative to the ESR, then the voltage your coil sees will be essentially nothing. What you have is essentially this:

schematic

simulate this circuit

For the current to increase, voltage across R1 must increase. Since the voltage across R1 plus the voltage across L1 must equal the capacitor's voltage, as the current increases, the voltage across L1 must decrease. That's bad for you, because it means you can ramp up the current in L1 less rapidly.

Furthermore, the heating caused by losses in the capacitor can damage the capacitor. That's also bad for you.

The capacitor datasheets will elaborate on these details. However, based on general characteristics of supercapacitors and electrolytics, I can tell you that the electrolytics will have a much lower ESR on average. Supercapacitors are intended for lower current applications, sitting somewhere between a battery and a capacitor. They will typically be damaged by high current, or at least their ESR will be so high they will not perform well in your application.

There are also particular electrolytic capacitors designed to have an especially low ESR. These are called simply "low ESR" capacitors. They are also more expensive, but you might look into them. They typically find application as ripple filters in power supplies, where a higher ESR in the constant charge-discharging cycle they do would be a problem for efficiency, performance, or reliability.

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  • \$\begingroup\$ "Supercapacitors are intended for lower current applications" - That's not always true. There are those "GoldCap" or whatever things with huge ESR, applicable for e.g. RTC backup power; but there are also those models like Maxwell's "BoostCap": 3000F @ 0.29 milliOhm ESR and max. pulsed current of 2200A (210A continuous) @ 2.7V. (Source: tecategroup.com/products/datasheets/maxwell/K2_series.pdf) \$\endgroup\$ – JimmyB Jan 18 at 13:35
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Added to PJC50's answer linked in the comments one has to look at the total specification of a component to find its applicable value to a project.

You are not looking at all the relevant data.

The supercap you are considering is not only just low voltage, it has a HUGE internal resistance compared to the high voltage ones. So, not only do you need the higher voltage to get past the resistance and reluctance (a coil will not conduct instantaneously, but build up current due to the voltage applied) of the electronic circuit, you need to avoid putting any extra resistance in where you can.

Not to mention most supercaps could be thrown away after the first try of putting even half an ampere instantaneous current into them or getting it out.

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