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Calculating the Total Energy Released by a Capacitor up to Defined Points in Time

Hi All,

First ever post here. I am not at all an electronics expert. In fact, I'm pretty useless, yet due to resource availability, this task has fallen on me.

Here is my situation. I currently have a device which, amongst other things, charges a capacitor such that on activation of a switch, the main power supply is removed and the capacitor kicks in which subsequently activates a pyrotechnic device used as part of a release mechanism.

Due to confidentiality reasons, I am not able to present the whole circuit diagram, but I have attached a modified snippet of the section of the circuit concerned. I'll be frank, I am not entirely sure of the function of the transistor, but I don't think this should influence my query too much. In terms of the pyro, in testing we have attached a 'dummy load' in the form of a resistor so I have been treating it as such. I guess for this purpose, the pyro can be viewed as a resistor.

Now, to get to my actual query. I have positioned a probe either side of the pyro/dummy load and connected to an oscilloscope which can give me a readout in terms of voltage or current. In both instances, on activation of the switches, the capacitor discharges and produces a discharge curve, as expected (a pretty typical looking exponential decay curve). What I am desperately trying to calculated is the total energy released up to certain time intervals (not that it impacts the process much, these time intervals are 5ms and 10ms). I have been told various things and despite using numerous attempts using various formulae and methodologies (lots of mentions of time constants, C=Q/V etc., E= I^2*R etc.), I have been unsuccessful. Historically we have used an automated programme produced by a subcontractor around 2 decades ago which did all the work for us once the device was plugged in. Unfortunately, this machine has now seen it's last days, so we need to find a manual method of it. The machine when it was working would produce a test certificate as a printout, which would present the required results. I have an extract of this certificate (attached) which provides currents and energies from which I have been trying to work backwards to try and figure out how they achieved the desired results. However, as I previously mentioned, I am failing terribly, so any guidance anyone can provide would be greatly appreciated!

circuit snip.png

cert snip.png
 
The transistor is acting as an electronically-controlled on/off switch.

The total energy in a capacitor is:

E = 1/2 x C x V^2 -- Energy equals one-half times the capacitance (in farads) times the square of the voltage.

The unit is watt-seconds, abbreviated Ws, or W-s

To calculate a partial energy, calculate it at the starting voltage and at the ending voltage, and subtract. Neither voltage has to be "fully charged" or "empty".

ak
 
Because Joule is a proper name, it is spelled out lower case (joule) but abbreviated with a capital letter (J).

ak

ps. I'm old, and I have old camera flashes. Watt-seconds are us.
 
Hi All,

First ever post here. I am not at all an electronics expert. In fact, I'm pretty useless, yet due to resource availability, this task has fallen on me.

Here is my situation. I currently have a device which, amongst other things, charges a capacitor such that on activation of a switch, the main power supply is removed and the capacitor kicks in which subsequently activates a pyrotechnic device used as part of a release mechanism.

Due to confidentiality reasons, I am not able to present the whole circuit diagram, but I have attached a modified snippet of the section of the circuit concerned. I'll be frank, I am not entirely sure of the function of the transistor, but I don't think this should influence my query too much. In terms of the pyro, in testing we have attached a 'dummy load' in the form of a resistor so I have been treating it as such. I guess for this purpose, the pyro can be viewed as a resistor.

Now, to get to my actual query. I have positioned a probe either side of the pyro/dummy load and connected to an oscilloscope which can give me a readout in terms of voltage or current. In both instances, on activation of the switches, the capacitor discharges and produces a discharge curve, as expected (a pretty typical looking exponential decay curve). What I am desperately trying to calculated is the total energy released up to certain time intervals (not that it impacts the process much, these time intervals are 5ms and 10ms). I have been told various things and despite using numerous attempts using various formulae and methodologies (lots of mentions of time constants, C=Q/V etc., E= I^2*R etc.), I have been unsuccessful. Historically we have used an automated programme produced by a subcontractor around 2 decades ago which did all the work for us once the device was plugged in. Unfortunately, this machine has now seen it's last days, so we need to find a manual method of it. The machine when it was working would produce a test certificate as a printout, which would present the required results. I have an extract of this certificate (attached) which provides currents and energies from which I have been trying to work backwards to try and figure out how they achieved the desired results. However, as I previously mentioned, I am failing terribly, so any guidance anyone can provide would be greatly appreciated!

View attachment 39630

View attachment 39629

I am using some made up values because you are indefinite about whether your circuit values are in joules or millijoules, amps or milliamps, etc. I am assuming the capacitor is energized to 100 volts, and a 1k0 resistor is switched across the cap at time t = 0.

The voltage equation for the cap is:
Tas142a.JPG
The standard de-energizing voltage curve for the cap with 1k0 across it
is:
Tas142b.JPG
The energy equation for the cap is:
Tas142c.JPG
The energy curve for the cap at a particular voltage is;
Tas142d.JPG
As you can see, the cap loses 9 joules of energy in the time interval of 0 to 2 secs. From 1 to 2 secs, it loses only 2 joules. After 4 secs, it is almost depleted of energy.

If you were to give me a more precise specification without revealing the family jewels, I could give you a more definite answer.

Ratch
 
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