Exploring a Capacitor Math Anomaly: Energy Transfer Between Two Capacitors

In summary, the conversation discusses a mathematical anomaly concerning the energy transfer between two capacitors. The experiment involved two capacitors, C1 and C2, with different specifications and a capacitor calculator was used to aid in the calculations. The non-polarized capacitors used in the test were of high quality and well within their tolerances. However, the results of the experiment showed a discrepancy in the amount of energy transferred between the two capacitors. The conversation also delves into the concept of conservation of energy and the effects of resistance on the energy transfer.
  • #1
nut case
3
0
I may have a mathematical anomaly concerning the energy transfer between two capacitors.

Here is the experiment:

CAPACITOR SPECS COULOMBS JOULES
CAPACITOR 1 aka C1
C1 11200UF@19V
@ 19V 212.8m 2.02 @17.48V 195.77m 1.71
TOTAL DISCHARGE 17.03m .31

CAPACITOR 2 aka C2
C2 1000UF@100V
TOTAL CHARGE/ C2@ 17.48V 17.48m .16

Capacitor calculator: http://highfields-arc.6te.net/constructors/olcalcs/caclchrg.htm

Note: All non-polarized capacitors (polypropylene dielectric- ESR rating of .1582ohms) used in test are of high quality and were well within their tolerances and should maintain at least 90 to 95% efficiency through out all testing cycles.

Wire leads used to connect components to circuit are the actual leads on the capacitors, installed by the manufacturer.


Test:

C1 (19v starting voltage) discharges directly into C2. Both capacitors equalize to an identical voltage of 17.48v within 1 second.

Note: According to the math, C1 discharged 17.03m coulombs @ .31 joules during this cycle directly into C2, which can only hold .16 joules @17.48v.

What happened to the remaining .15 joules during this energy transfer?

This one has me wondering!

Thanks for any help guys!
Brad
 
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  • #2
The conserved quantity is Coulombs. Work out the energy balance with resistive wires (include the energy loss in the wires), and then take the limit as the wire resistance goes to zero.

Bob S
 
  • #3
  • #4
If you discharge a perfect capacitor through wire of no resistance into another capacitor you will produce a resonant circuit that will 'ring' for ever - energy sloshing from one capacitor into the other and back because of the inherent inductance in the construction. The only thing which will eventually cause the oscillations to decay will be radiation of em into space.
 
  • #5
Another problem might help illustrate this further. Suppose we have a 1 kilo cannonball traveling at 10 m/s. It has 10 units of momentum and 50 Joules of kinetic energy. Let's say this cannonball embeds into a 10 kilo block of wood that is resting on a frictionless surface. Because it embedded, all the momentum is now carried by combined mass of the two objects. The momentum is 10 and the new mass is 11 kilos. That means the new speed is 10/11 ~ 0.9 m/s. That means that it now has ~4.5 Joules of kinetic energy. 45.5 Joules have disappeared, maybe.

That's a substantial energy loss. If you actually did this experiment (or something similar with pendulums) the place that the energy goes will become obvious. It turns into sound waves. Remember that energy can transform. Sometimes, the only things that we can be sure haven't left confines of our problem will be things like momentum, charge, current, etc.
 
  • #6
Thanks Guys
excellent info.
Do any of you know anything about the "capacitor paradox".
After a little research, found this... Could this be what I'm up against?If I'm breaking off the original question to much, let me know and I will start a new thread if needed.

Thanks Brad
 
  • #7
Yes. The paradox is only there if you neglect the real world losses - resistance and radiation.
 
  • #8
When performing the above experiment with larger Capacitors and assorted loads/resistors and a calorimeter--
I have observed the following results:
For example,
when discharging C2 (17.48v to 0v) through load to ground, consistently produced around 95-98% as much heat when compared to
C1 (19v to 17.48v) discharging through load to ground

I looked at this as C2 (at 17.48v) storing approx. 98% of energy discharged from C1.
Is this correct? Just want to be sure..

Thanks Brad
 
  • #9
The energy stored will be half C Vsquared. Do the sums for before and after conditions and see what you'd expect to get.
You haven't quoted capacitor values so you'll have to work yourself, it out using those values. You can be pretty sure that your measurements will agree with theory - minus a bit for losses that your calorimeter hasn't caught. Calorimetry is unreliable unless you have high class kit.
 
  • #10
nut case said:
Here is the experiment:

CAPACITOR SPECS COULOMBS JOULES
CAPACITOR 1 aka C1
C1 11200UF@19V
@ 19V 212.8m 2.02 @17.48V 195.77m 1.71
TOTAL DISCHARGE 17.03m .31

CAPACITOR 2 aka C2
C2 1000UF@100V
TOTAL CHARGE/ C2@ 17.48V 17.48m .16

Capacitor calculator: http://highfields-arc.6te.net/constructors/olcalcs/caclchrg.htm

Note: All non-polarized capacitors (polypropylene dielectric- ESR rating of .1582ohms) used in test are of high quality and were well within their tolerances and should maintain at least 90 to 95% efficiency through out all testing cycles.

Brad are you sure about that, 11200 uF non polarized polypropylene capacitor. That is an enormous capacitance for that type of capacitor. The largest polypropylene caps I’m aware of are motor start capacitors and they usually go up to about 100uF. I would have expected that you’d only find 11200uF in an electrolytic capacitor. Where did you get such a large polypropylene non polarized capacitor and physically how large is it?
 
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  • #11
Let's look at this problem from the standpoint of conservation of energy, first with a series resistance R between the two capacitors when C1 (11,200 uF @ 19 volts) is discharged into C2 (1000 uF @ 0 volts). The series equivalent capacitance of C1 and C2 is 918 uF, which I will call C3. Initially, the voltage between the two capacitors is 19 volts, and the initial power dissipated in R = 192/R. The total energy E dissipated in R during the complete discharge of C1 into C2 is

E = ∫o∞V(t)2/R dt =192∫o∞e-2t/τ/R dt = 192·τ/2·R

where V(t) = 19 e-t/τ and τ = R·C3

So E = 192R·C3/2·R = 192·C3/2 which is independent of R !

So the total dissipated energy is 192 x 918 x 10-6/2 = 0.165 Joules, independent of R. So even when R -> zero, there is energy dissipated during the charge transferred from C1 to C2. Charge (number of electrons) is conserved.

Bob S
 
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Related to Exploring a Capacitor Math Anomaly: Energy Transfer Between Two Capacitors

1. What is a capacitor and how does it work?

A capacitor is an electrical component that stores energy in an electric field. It is made up of two conductive plates separated by an insulating material, called a dielectric. When a voltage is applied to the capacitor, one plate becomes positively charged and the other becomes negatively charged, creating an electric field between them. This electric field stores energy, which can be released when the capacitor is connected to a circuit.

2. What is the math anomaly in energy transfer between two capacitors?

The math anomaly in energy transfer between two capacitors refers to a discrepancy in the calculation of energy transferred between two capacitors in series versus in parallel. According to traditional calculations, the energy transferred in parallel is twice as much as in series, but experimental results have shown that this is not always the case.

3. What factors contribute to the math anomaly in energy transfer between two capacitors?

There are several factors that can contribute to this math anomaly, including the presence of resistance in the circuit, the dielectric material used in the capacitors, and the specific circuit configuration. Additionally, the assumptions made in traditional calculations, such as ideal conditions and no energy loss, may not hold true in real-world scenarios.

4. How can this math anomaly be resolved?

There is ongoing research and debate on how to resolve this math anomaly. Some proposed solutions include incorporating non-ideal factors into the calculations, using more accurate models for energy transfer, and conducting more precise experiments to gather data. Ultimately, a combination of these approaches may be necessary to fully resolve the discrepancy.

5. What are the potential implications of this math anomaly?

The implications of this math anomaly could have significant effects on the design and efficiency of electronic circuits and devices. If the traditional calculations are not accurate, it could lead to unexpected results and potentially impact the functionality and performance of these systems. Therefore, further research and understanding of this anomaly are crucial for advancing our understanding of energy transfer in electronics.

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