Does a battery exert energy keeping a capacitor charged?

I am researching whether or not there is an equation that calculates energy used by a DC battery to keep a capacitor charged over time in a capacitor circuit.

I know a capacitor in a circuit acts as a break when it is fully charged, but does the battery continue using energy to keep the capacitor charged once it is fully charged?

berkeman
Mentor
I am researching whether or not there is an equation that calculates energy used by a DC battery to keep a capacitor charged over time in a capacitor circuit.

I know a capacitor in a circuit acts as a break when it is fully charged, but does the battery continue using energy to keep the capacitor charged once it is fully charged?
Welcome to the PF.

It depends on the type of capacitor. All real capacitors will have a small "leakage current", which the battery has to supply to keep the cap from self-discharging over time. You can do a search on capacitor leakage current to see what typical values for different types of caps (electrolytic, tantalum, ceramic, etc.).

Welcome to the PF.

It depends on the type of capacitor. All real capacitors will have a small "leakage current", which the battery has to supply to keep the cap from self-discharging over time. You can do a search on capacitor leakage current to see what typical values for different types of caps (electrolytic, tantalum, ceramic, etc.).

The type of capacitor I'm talking about is a parallel plate capacitor C = keA/d where k is the dielectric constant, e is 8.85*10^-12, A is the area of the plates, and d is the distance between the plates.

Assuming no leakage, I want to know in a theoretical sense whether or not a capacitor continues to need the battery to "push" protons onto its plate.

Intuitively, I assume that the battery has to exert energy to keep the protons pushed up against the capacitor plate, because the protons are attracted to the electrons on the opposite plate, and the "path of least resistance" is back through the wires and back through the battery.

I'm looking for an equation that depends on time, emf, capacitance that calculates the energy needed to keep the capacitor fully charged in the form of E(t) = ... where E(t) is the total energy exerted keeping the protons on the plate at time t

berkeman
Mentor
The type of capacitor I'm talking about is a parallel plate capacitor C = keA/d where k is the dielectric constant, e is 8.85*10^-12, A is the area of the plates, and d is the distance between the plates.

Assuming no leakage, I want to know in a theoretical sense whether or not a capacitor continues to need the battery to "push" protons onto its plate.

Intuitively, I assume that the battery has to exert energy to keep the protons pushed up against the capacitor plate, because the protons are attracted to the electrons on the opposite plate, and the "path of least resistance" is back through the wires and back through the battery.

I'm looking for an equation that depends on time, emf, capacitance that calculates the energy needed to keep the capacitor fully charged in the form of E(t) = ... where E(t) is the total energy exerted keeping the protons on the plate at time t
No leakage = no current flow.

So a battery hooked up to a capacitor will run out of energy no faster than a battery hooked up to nothing? I guess in this case there's "backwards leakage" from the plate towards the battery

berkeman
Mentor
So a battery hooked up to a capacitor will run out of energy no faster than a battery hooked up to nothing? I guess in this case there's "backwards leakage" from the plate towards the battery
For the ideal situation you are asking about, that's correct. Once the cap is charged up, you can disconnect it from the battery and both will stay at that final voltage.

Just keep in mind that all real-world capacitors and batteries have leakage currents. That's why real battery storage life is not infinite, and why real capacitors don't stay charged up forever.

berkeman
Mentor
I guess in this case there's "backwards leakage" from the plate towards the battery
TBH, I don't know what you mean by that... No current flows.

sophiecentaur
Gold Member
Just keep in mind that all real-world capacitors and batteries have leakage currents.
It would be better to disconnect the battery, once the capacitor was charged. (Ignoring leakage, even through dampness in the air etc)

"backwards leakage" means leakage from one plate towards the other passing through the battery

I'm asking because I am trying to figure out where energy is being used in an HHO generator, which essentially uses parallel plate capacitors in parallel.

According to this discussion the efficiency of generating oxyhydrogen using the HHO method should be very high given that after charging plates, the only energy usage is keeping the plates charged because of leakage

Does anyone know the efficiency of HHO generators btw?

berkeman
Mentor
"backwards leakage" means leakage from one plate towards the other passing through the battery

I'm asking because I am trying to figure out where energy is being used in an HHO generator, which essentially uses parallel plate capacitors in parallel.

According to this discussion the efficiency of generating oxyhydrogen using the HHO method should be very high given that after charging plates, the only energy usage is keeping the plates charged because of leakage

Does anyone know the efficiency of HHO generators btw?
What's an HHO generator? Do you mean a fuel cell? Or just splitting water into O2 and H2 using electricity?

berkeman
Mentor
Or do you mean like the MythBusters HHO Generator...

What's an HHO generator? Do you mean a fuel cell? Or just splitting water into O2 and H2 using electricity?

I'm not sure what you mean by fuel cell, but if your talking about converting hydrogen and oxygen until electricity like Honda's hydrogen car's engine does then no.

There's a lot of content on the internet about it I'm not sure which link to give you cuz I'm not referring to anything in particular. Maybe mythbusters? Although I'm on my phone right now and can't figure out how to get a working link.

I found this on eBay

Or do you mean like the MythBusters HHO Generator...

Yes this, haven't watched that video yet, I'm at the cheesecake factory

berkeman
Mentor

berkeman
Mentor
Thread reopened. After a detailed PM conversation, it does not appear that the OP is asking about over-unity.

To clear things up, I know 1 mol of water requires 237kJ of energy to dissociate into hydrogen and oxygen plus 49kJ to overcome the change in entropy of the reaction, and I know you get 237+49=286kJ of energy back from combusting the hydrogen and oxygen back into water.

I'm trying to dissect how the HHO generator is working, because I go to New Jersey Institute of Technology, and I have a capstone engineering course I have to take in a year or so, which is sort of like an undergraduate thesis, and I'm trying to figure out what topic I want to pursue.

I have an alternative, but similar proposition to approach electrolyzing water, but before I go and tell my professor it's what I want to work on, I want to have a decent understanding of the topic.

I have a few questions about the HHO generator, which if you want to know more about I recommend watching

One question I have is how efficient these generators are, and to calculate that simply divide energy output by energy input and multiply by 100.

The king of random channel that I linked claims 5 Liters per minute, but even accounting for the fact that there are 55.5 moles per liter of water, don't we need to know the resistance in the system to find the heat dissipation?

Can i suggest you Google the efficiency of electrolysis. Lots of research has been done on this. For example..

https://en.m.wikipedia.org/wiki/Electrolysis_of_water#Efficiency
yeah, i'm doing that now. i just discovered a mole of hydrogen fills up about 22 Liters of space, which goes against what I initially assumed.

So i just watched this guy test a Punch 5.0 HHO generator, which claimed near 100% efficiency

and I used his voltage, current, and time measurements to calculate the energy input. He produced 1 liter of hydrogen gas, which is 0.044643 moles, because 1 mol H2 = 22.4L

The Input energy = V*i*t= (14.13V)(9.845A)(109s)=15163J

The output energy (from combusting the hydrogen is potentially) = n*H = (0.044643 moles H2) * (237.5 kJ/mol) = 10602.7 J

The efficiency is therefore output/input = 10602.7/15163 *100% = 70%

I wasn't sure whether I should use 237.5 kJ/mol, or 286 kJ/mol for the combustion output energy of hydrogen gas, but in either case, if I was supposed to use 286 kJ then the efficiency of the Punch 5.0 is 84.2%

Did I do this right? thoughts?

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berkeman
Mentor
The Input energy = V*i*t= (14.13V)(9.845A)(109s)=15163J

The output energy (from combusting the hydrogen is potentially) = n*H = (0.044643 moles H2) * (237.5 kJ/mol) = 10602.7 J

The efficiency is therefore input/output = 15163/10602.7 *100% = 70%
Efficiency is Output / Input, so I'm not sure how you got the right answer with your math, but whatever.

Efficiency = 10602 / 15163 = 0.699 = 70%

So it's better to use the electricity directly if possible, instead of storing the energy as Hydrogen. If you have a hydroelectric dam and want to power your car with it, then the efficiency difference between using batteries for storage versus Hydrogen and fuel cells is worth considering...

Efficiency is Output / Input, so I'm not sure how you got the right answer with your math, but whatever.

Efficiency = 10602 / 15163 = 0.699 = 70%

So it's better to use the electricity directly if possible, instead of storing the energy as Hydrogen. If you have a hydroelectric dam and want to power your car with it, then the efficiency difference between using batteries for storage versus Hydrogen and fuel cells is worth considering...

Yeah, I put input/output, and 15163/10602 but i meant the inverse. Thanks.

And in terms of cars, yeah you make a valid point, but for now I'm just looking for the most efficient way to convert electrical energy into hydrogen gas, because there are other uses for them; rocket propulsion being one

berkeman
Mentor
Yeah, I put input/output, and 15163/10602 but i meant the inverse. Thanks.

And in terms of cars, yeah you make a valid point, but for now I'm just looking for the most efficient way to convert electrical energy into hydrogen gas, because there are other uses for them; rocket propulsion being one
Interesting. What are some other ways to get Hydrogen? Do they all start with water?

berkeman
Mentor
BTW, I think you can increase the efficiency of electrolysis some by adjusting the ionic content of the water. Have you already looked at that?

no they don't wall start with water, but water covers 70% of the surface of this planet

there's other ways of getting hydrogen, like through gasification, which is when high temperature steam reacts with methane, or something, but other methods of getting hydrogen haven't been introduced to me in my curriculum, so i wouldn't really know about them

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BTW, I think you can increase the efficiency of electrolysis some by adjusting the ionic content of the water. Have you already looked at that?
i saw that too, yeah.

that's like a final step sort of thing after i design the system, and the fundamentals are finalized i'd probably do control tests to compare different electrolytes