Everyone,
I think I found my hypothesis,

If a these capacitors are charged at 1.5 volts, then the tantalum will reach its max capacity the fastest.

This is because the tantalum has a small head, so it is easier for it to charge. Additionally, in general (I think) tantalum has a small ESR.
Can anyone confirm whether my hypothesis is a good one, and my explanation is correct?
Additionally, I made up a small experiment to see if my test will work. And it did!

Two big issues.

First, your hypothesis is based on a claim that, even if the tantalum capacitors charge faster, the data can't be used to support the claim. They could be faster for a completely different reason that has nothing to do with the size of the head. So unless your experiment allows you to address the issue of whether head size has actually is a significant factor, don't even go there.

Second, your experiment most certainly did NOT work. You have a resistor in series with the capacitor. I'm willing to bet that this is there in order to slow the response down enough so that you can actually time it. The problem is that, in doing so, you have made your data meaningless with regards to the the purpose of the experiment. I can't tell for sure, but that looks like an 18 Ω resistor. Let's say that your two capacitors have ESRs of 0.1 Ω and 0.2 Ω -- in other words, a factor of two difference. Assuming (and this is NOT a reasonable assumption) that all other variables are exactly the same between the two, the time constant between your two tests will only vary by about 0.5%. Let's say that you have a 1000 μF capacitor. Five time constants is going to be 90.5 ms with one capacitor and 91.0 ms with the other. Can you REALLY reliably make measurements that can distinguish the difference?

And remember those bad assumptions? With your set up, just changing from one capacitor to another is likely to introduce a change in total series resistance that is larger than the ESR of the capacitors, let along the difference in the ESRs, which is what you are really interested in.

And the assumption that both of your capacitors have the same capacitance is a hugely bad assumptions. Capacitors typically have large tolerances and electrolytics (such as tantalums) tend to be among the worst with ±20% being very common.

So let's say that one of your capacitors, the low ESR one, is just 5% high and the other is 5% low. So now five time constants of the "fast" capacitor is 95.0 ms while for the "slow" one it is 86.5 ms.

How are you actually making your time measurement?

Trying to measure from 0 V to 4.99 V is NOT the way to go. There is WAY too much uncertainty at either end.

The usual way to make these kinds of measurements is from some low threshold to some high threshold, with 10% to 90% being very common; so common, in fact, that the graticule (screen markings) on most oscilloscopes is specifically marked to make this type of measurement easy.

 

Well, I chose it, and the teacher approved, and I'm sorta stuck with it. I mean, I'm just looking for advice on my hypothesis, I can definitely carry out the test.

Does it have to be just on capacitors in general, or on "which type of capacitor charges fastest" specifically?

I think you are biting off more than you can chew given your grade level and the equipment you really need to make the necessary measurements.

You might consider something more manageable from a measurement standpoint, such as characterizing the capacitance distribution under various conditions. For instance, pick a particular capacitance value that is available in various types with the same tolerance (I'd recommend either 10% or 20%). Choose ones that are inexpensive. Then purchase a good quantity of them (say 50 to 100 in each set) getting some of the exact same brand and part number but from different distributors and the same type from different manufacturers. Then put them all (in separate containers -- keep them in their respective sample sets) into an insulated container and let them sit for a couple days in a place that has a pretty stable temperature. Then measure the capacitance of all of them with a capacitance meter. Plot the min/max/mean/stddev for all the samples. What observations can you make?

If you can ditch the capacitor thing altogether, a nice project would be to explore the effect of thermal runaway in LEDs that share a single current-limiting resistor. It's an easy experiment to set up and, given the number of folks on this site that are always asking about it, you could probably publish your results as a Tech Article here (maybe even get paid for it).

 

The oscilloscope can be used to time it, and the Keysight PSU is what I will use to set the output voltage.
How would you have my set the HP oscilloscope so that when the capacitor is charged, it gives an accurate reading of the time to maximum charge?

 

Who's equipment is this? It certainly is NOT yours. Having $20,000US of PROFESSIONAL equipment isn't something the average 8th grader has on their bench.

 

Who's equipment is this? It certainly is NOT yours. Having $20,000US of PROFESSIONAL equipment isn't something the average 8th grader has on their bench.

It's CSUN's. My dad works there, and he got permission from an associate to use it for my expirement.

 

You can have $20,000 worth of equipment and still don't know how to use it, regardless of age.

What TS has is not the correct equipment to conduct this science project and the TS doesn't even know it.

What TS needs is a square wave generator and an oscilloscope.

 

What TS needs is a square wave generator and an oscilloscope.

And good ones with good leads etc. to boot, if you want to make meaningful measurements and comparisons of capacitors.

Wondering out loud:

What if the hypothesis is, "If electrolytic capacitors are 'slow' compared to ceramic capacitors, then the latter will do a better job of filtering out high frequency noise"? The experiment would then be to feed a high frequency signal across the two types of capacitor, both sized at ~1µF where both types can be purchased, and observe with the oscilloscope how much signal passes.

Hardware heavy for 8th grade but it appears he may have access to what he needs.

 

Hardware heavy for 8th grade but it appears he may have access to what he needs.

Yep. CSUN has the stuff I need.

 

Yep. CSUN has the stuff I need.

Why are you just now deciding on telling us this?

 

Why are you just now deciding on telling us this?

Probably because he's in eighth grade and this is all very new to him and he doesn't know what he should tell us and what is irrelevant. We were pretty much all in that mode at one time, even though it can be hard to remember those days.

 

Probably because he's in eighth grade and this is all very new to him and he doesn't know what he should tell us and what is irrelevant. We were pretty much all in that mode at one time, even though it can be hard to remember those days.

If actually didn't even know CSUN had this stuff until a couple days ago, when I was talking to my dad.
Know that you know what's available to me how would you recommend carrying out the expirement/testing (as in how I should lay out the circuit, how I should get the readings via oscilloscope.

 

If actually didn't even know CSUN had this stuff until a couple days ago, when I was talking to my dad.
Know that you know what's available to me how would you recommend carrying out the expirement/testing (as in how I should lay out the circuit, how I should get the readings via oscilloscope.

I still wouldn't recommend this project. You might read up on some of the issues, even for manufacturers, in making ESR measurements. One place to start might be:

https://www.mouser.com/pdfdocs/MethodsandProblemsmeasuringESR.pdf

You don't need to follow everything to get the gist of problems.

 

I still wouldn't recommend this project. You might read up on some of the issues, even for manufacturers, in making ESR measurements. One place to start might be:

https://www.mouser.com/pdfdocs/MethodsandProblemsmeasuringESR.pdf

You don't need to follow everything to get the gist of problems.

This is gonna make me sound stupid, but, just to be clear, if I found the ESR of the capacitors without a problem (problems being "notoriously hard to measure"), that would be the testing completed, right?

 

This is gonna make me sound stupid, but, just to be clear, if I found the ESR of the capacitors without a problem (problems being "notoriously hard to measure"), that would be the testing completed, right?

Not quite sure I understand the question you are asking.

Is the "testing" you are referring to the tests needed to address your question of which capacitors reach full charge the fastest?

There are many ways to estimate ESR from measurements. Some of them are better than others. For some applications we don't need an accurate measurement at all, but just something that gives a ballpark figure. For testing your hypothesis, you would need very accurate measurements capable of detecting differences between ESRs in the milliohm range. Not easy to do. Complicating this significantly is the fact that ESR is not a single number for a given capacitor, even at a constant temperature. It changes with voltage and, even more importantly, it changes with frequency. You are are really trying to explore how fast a capacitor can charge, you are dealing with extremely high frequency signals. For instance, the time constant of a 1 μF capacitor with a 2 mΩ ESR is 2 ns and you are talking frequency components in the 100 MHz range.

Whatever means you use to measure ESR, you will need to validate those methods by measuring the ESRs of a bunch of capacitors and then comparing the results to some kind of a reference, which could be the component data sheets or it could be another measurement instrument of known performance.

 

Is the "testing" you are referring to the tests needed to address your question of which capacitors reach full charge the fastest

Yes, the when I say "testing" I mean expirements to answer the question.

 

Not quite sure I understand the question you are asking.

Is the "testing" you are referring to the tests needed to address your question of which capacitors reach full charge the fastest?

There are many ways to estimate ESR from measurements. Some of them are better than others. For some applications we don't need an accurate measurement at all, but just something that gives a ballpark figure. For testing your hypothesis, you would need very accurate measurements capable of detecting differences between ESRs in the milliohm range. Not easy to do. Complicating this significantly is the fact that ESR is not a single number for a given capacitor, even at a constant temperature. It changes with voltage and, even more importantly, it changes with frequency. You are are really trying to explore how fast a capacitor can charge, you are dealing with extremely high frequency signals. For instance, the time constant of a 1 μF capacitor with a 2 mΩ ESR is 2 ns and you are talking frequency components in the 100 MHz range.

Whatever means you use to measure ESR, you will need to validate those methods by measuring the ESRs of a bunch of capacitors and then comparing the results to some kind of a reference, which could be the component data sheets or it could be another measurement instrument of known performance.

You know, it is an option for my project to be able to instead of max capacity, I can measure time constants. I was thinking it could possibly be based on the Keysight video...?:

I'm unsure if what they were doing would work, and what resistor would I use for a .47uf capacitor?

 

There's quite a bit of sloppy terminology, but the basic idea is right.

The traditional way to take the measurement is to use a square wave drive signal whose period is at least ten time constants, which can be approximated by just slowing the drive signal down until the response signal appears to be fully settled. You then adjust the scale of the waveform so that it goes the full vertical scale of the screen. You then adjust the time base to the slowest rate that keeps the waveform on the screen between the 10% and 90% points. Then you measure this time, which is equal to 2.2 time constants. Each of these steps is intended to make for a more accurate measurement.

In theory you can use any resistor value you want, but in practice there are issues if you go either too big or too small. Too big and the leakage current of the capacitor becomes a problem (and this depends on the type of capacitor) and too small and the finite output impedance of your signal source becomes an issue that can't be ignored. For a 0.47 μF capacitor you have a pretty wide range of reasonable resistor values you can use. You probably start with 1 kΩ which would put your 10%-90% rise time in the 1 ms range. Part of your experiment could be the dependence of the results (or the departure of the observed results from those expected) on the resistance chosen. Pick different types of capacitors and different values (say multiples of 10 over a fair range) and plot the percent deviation of the observed time constant from the observed time constant. Here you have to obvious null hypotheses -- first that there is no deviation at all and second that the deviation is independent of the capacitor type.

 

There's quite a bit of sloppy terminology, but the basic idea is right.

Well hey, 8th grader here, don't judge me. Despite being in a HGM school, I still don't understand half the things you talk about

For the wide range of capacitors, does it matter the voltage maximum of each one? It shouldn't because I'm only running 1.5v, so if I don't exceed that, I should be fine, right?

I'm unclear on the null, though, are you talking about deviation from the estimated time? Because if I put that in my hypothesis, that isn't an answer to which capacitor charges the fastest.

 

Well hey, 8th grader here, don't judge me. Despite being in a HGM school, I still don't understand half the things you talk about

Oh, I'm not judging you at all. Just pointing out that the video is pretty sloppy about a number of things. The presentation is such that people that don't already know the concepts are unlikely to spot the sloppiness, so absolutely nothing for you to feel bad about.

For the wide range of capacitors, does it matter the voltage maximum of each one? It shouldn't because I'm only running 1.5v, so if I don't exceed that, I should be fine, right?

In theory it doesn't matter (provided you don't exceed the rated working voltage). But that could be another thing that you include in your hypothesis and then use different voltages and see if it does. In general, the larger the voltage the better the measurement (that's true in most things -- the larger the signal the more accurately it can usually be measured).

I'm unclear on the null, though, are you talking about deviation from the estimated time? Because if I put that in my hypothesis, that isn't an answer to which capacitor charges the fastest.

I thought you had moved away from trying to answer that question and were formulating a new line on inquiry. Sorry for misunderstanding.

Measuring the time constant of an RC circuit like this in order to find the ESR of the capacitor is NOT going to produce meaningful results. I explained why in an earlier post.

Let's see if I can come up with an analogy that might make the reason a bit more obvious.

Imagine you have two pieces of half-inch thick foam rubber that has paper glued to one side (the foam is the capacitor and the paper is the ESR of the capacitor) and you want to know which piece of paper is thinner (which capacitor has the lower ESR). You know that the paper is somewhere between 3 and 5 mils thick. The thickness of the foam can vary by up to 20% in either direction from the nominal half-inch. You don't have anything that can measure less than an inch thick, so you take a ream of paper (this is the resistor) and put the first pieces of foam rubber on it and measure the thickness and find it to be 1.93 inches. You then do the same with the other and find it to be 2.09 inches. Do you really believe that the paper on the first piece is well over one-eighth of an inch thinner than the piece of paper on the second?

If someone else did things this way and then tried to make that claim, how would you explain to them that they have some problems with their approach?

 

Oh, I'm not judging you at all. Just pointing out that the video is pretty sloppy about a number of things. The presentation is such that people that don't already know the concepts are unlikely to spot the sloppiness, so absolutely nothing for you to feel bad about.



In theory it doesn't matter (provided you don't exceed the rated working voltage). But that could be another thing that you include in your hypothesis and then use different voltages and see if it does. In general, the larger the voltage the better the measurement (that's true in most things -- the larger the signal the more accurately it can usually be measured).



I thought you had moved away from trying to answer that question and were formulating a new line on inquiry. Sorry for misunderstanding.

Measuring the time constant of an RC circuit like this in order to find the ESR of the capacitor is NOT going to produce meaningful results. I explained why in an earlier post.

Let's see if I can come up with an analogy that might make the reason a bit more obvious.

Imagine you have two pieces of half-inch thick foam rubber that has paper glued to one side (the foam is the capacitor and the paper is the ESR of the capacitor) and you want to know which piece of paper is thinner (which capacitor has the lower ESR). You know that the paper is somewhere between 3 and 5 mils thick. The thickness of the foam can vary by up to 20% in either direction from the nominal half-inch. You don't have anything that can measure less than an inch thick, so you take a ream of paper (this is the resistor) and put the first pieces of foam rubber on it and measure the thickness and find it to be 1.93 inches. You then do the same with the other and find it to be 2.09 inches. Do you really believe that the paper on the first piece is well over one-eighth of an inch thinner than the piece of paper on the second?

If someone else did things this way and then tried to make that claim, how would you explain to them that they have some problems with their approach?

Well, the analogy helped. As long as my question is vaguely related to capacitors, I don't think the teacher would care if I changed the question I am trying to answer. If the current question is a weird/untestable one, then if you were my age, and were doing a sci fair project on charging capacitors, what question would you have done?