Super capacitor analysis

Thread Starter

k1ng 1337

Joined Sep 11, 2020
436
Hi please consider the two circuits included in the image;

Concerning Circuit A:

1) How many joules are required to operate this circuit for one hour?

Concerning Circuit B - Let us assume the capacitor is fully charged to 3v:

2) How long will the circuit operate before the voltage on the capacitor drops below 2v? How many joules are consumed and how many remain in the capacitor? Let us assume the circuit cuts off below 2v.

3) As the capacitor discharges, what expression describes the current through the circuit?

4) As the capacitor discharges, how does the voltage across R2 respond?

5) As the capacitor discharges, how does the voltage across D2 respond?

I am looking for the equations to describe the above phenomenon over a simulation that just spits out the answer. Specifically I am interested in the different methods to calculate the energy available in the capacitor and the amount of work it can do before some threshold is reached. Alternatively I would like to predict the state of charge by measuring it's voltage / current either directly or elsewhere in the circuit via deduction.

Thanks! This is not homework :)
 

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Last edited:

Irving

Joined Jan 30, 2016
2,549
Concerning Circuit A:

1) How many joules are required to operate this circuit for one hour?
Watts = Joules/sec, so Joules = Watt Seconds.
Watts = V I = I^2 R = V^2/ R

Current through circuit, ILED = (V1 - Vf)/R1 = ?
Watts = V1 x ILED = ?
Joules = Watts x 3600 = ?

Concerning Circuit B - Let us assume the capacitor is fully charged to 3v:

2) How long will the circuit operate before the voltage on the capacitor drops below 2v? How many joules are consumed and how many remain in the capacitor? Let us assume the circuit cuts off below 2v.

3) As the capacitor discharges, what expression describes the current through the circuit?

4) As the capacitor discharges, how does the voltage across R2 respond?

5) As the capacitor discharges, how does the voltage across D2 respond?
The current through the LED is non-linear wrt voltage. You need the Vf v If chart of the specific LED to assess accurately.

For the capacitor charge Q = C Vc (so 100F charged to 3v = ? Joules)
Also ΔQ = I Δt therefore C ΔVc = I Δt

Finally I = (Vc - Vf)/R2

Because If v Vf is non-linear its difficult to write an equation for this. Piecewise approximation can be used, starting at
Vf = 2, Vc =3 therefore I(0) = (3 - 2)/100 = 10mA
After 1 sec, ΔQ = 0.01 Δt = 0.01Coulomb so ΔVc = 0.01/C = .0001, Vc(1) = 3 - .0001 = 2.9999V, i(1) = (2.9999 - 2)/R2 = 9.999mA, Vf(2) (from If/Vf chart) = (say)1.999v
After 2 sec, ΔQ = 0.009999 Δt = 0.009999Coulomb ΔVc = 0.00009999, Vc(2) = 2.9999 - .00009999 = 2.9998V, i(2) = (2.9999 - 1.999)/R2 = 10.009mA, Vf(3)= .... and so on...
 

Thread Starter

k1ng 1337

Joined Sep 11, 2020
436
Thank you Irving for the reply. I made this thread in an attempt to see how an engineer would work out the problem.

I am interested in capacitors primarily for the ability to predict their state by using relatively simple equations as opposed to the complex science of batteries. I am considering making a sizeable purchase of super caps or making my own carbon based in large size, either would make for a very interesting project.

Anyone have experience making capacitors? Aside from vacuum sealing I have been thinking about making one in very large size, perhaps as big as a piece of plywood and isolating it. I come across many materials with my job that are going to the landfill that could be easily fashioned into layered capacitors with the electrolyte being the major obstacle even with salt water.

Very cool stuff.
 
Last edited:

Irving

Joined Jan 30, 2016
2,549
Thank you Irving for the reply. I made this thread in an attempt to see how an engineer would work out the problem. Once again this site posted my message before I was done with it
Measuring capacitor voltage is a direct measure of SoC. Monitoring ΔV will give rate of discharge and a clue to time to run.
 

MrAl

Joined Jun 17, 2014
8,872
Hi please consider the two circuits included in the image;

Concerning Circuit A:

1) How many joules are required to operate this circuit for one hour?

Concerning Circuit B - Let us assume the capacitor is fully charged to 3v:

2) How long will the circuit operate before the voltage on the capacitor drops below 2v? How many joules are consumed and how many remain in the capacitor? Let us assume the circuit cuts off below 2v.

3) As the capacitor discharges, what expression describes the current through the circuit?

4) As the capacitor discharges, how does the voltage across R2 respond?

5) As the capacitor discharges, how does the voltage across D2 respond?

I am looking for the equations to describe the above phenomenon over a simulation that just spits out the answer. Specifically I am interested in the different methods to calculate the energy available in the capacitor and the amount of work it can do before some threshold is reached. Alternatively I would like to predict the state of charge by measuring it's voltage / current either directly or elsewhere in the circuit via deduction.

Thanks! This is not homework :)

Hello,

If you know the starting voltage across the capacitor and the ending voltage across the capacitor you can use the formula for the energy expended during those two voltage levels using the well known formula for energy in a capacitor.
 
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