(To the unsuspecting Reader: This is a story unfolding, which is frequently interrupted by interruption of my access to the interweb. Your travelling Webmaster)
Sounds like the title of a detective story, as a matter of fact, this story is a search for something missing. Before jumping to conclusions, we have to be clear about the word missing. There is a possibility of something being really absent, but it might be equally true that we simply percieve something to be absent, when in fact it is not. It all depends on the method of observing. And that brings us straight to the core of the problem.
If we decide we want to know the value of something, we usually have a gadget to measure that something. (Bless the 21st century)
To be more precise, when one wants to measure voltages, one uses a gadget called a Voltmeter.
When measuring Amperes (Amps in newspeak) one uses an Ampere meter. And to join this duo, we might as well introduce the 3rd illustrious cousin: the Ohm.
And since they all depend on each other, and are often used together, some smart kid decided long ago, that it would be a neat idea to stick gadgets to measure those three friends in a single box. (I’m simplifying, hope you will understand that!)
Fast froward to the digital age, and we figured out a way to get rid of that Meterthingy ( The nice big box with the moving needle) and replace it with something ‘digital’, a chip. And so the DVM was born. (Digital Volt Meter) .
But first, lets talk about the Volts and Amps and Ohms a bit.
It all started because some bloke in ancient Mesopotanie decided to put some bits of metal in a jar (http://en.wikipedia.org/wiki/Baghdad_Battery) and call that a battery. We still are not 100% sure wheather they actually used these batteries to fly their model airplanes, but judging by the hieroglyphics discoverd, one would not be too surprised if they if fact did. But that’s another story.
So the fellow (lets call him Ahmed, because he likely had a name, and it could well have been Ahmed), Ahmed then, was wondering how strong the juice was that his batteries produced. The tongue test was ok, but when you put 20 jars in series, this test resulted in some strange effects: his wife was unable to talk for days or weeks, depending on the amount of jars used for the test. (Yes, dear reader, of course Ahmed asked his wife to be the tester, since she had a far better ‘feel’ for these things.) Needless to say, eventually the misses decided she had enough of Ahmed’s battereeeeh tests, and left him for a rich merchant. Ahmed being the inventive soul, decided that something more reliable was needed to measure the properties of the the jarjuice.
He had by now worked out that there were actually 2 main properties involved with his juicejars. The one that determined how long the missus would be quiet, he called Voltage (this word has of course been translated from ancient Mesopotaniaspeak for the benefit of you, dear reader), and the one that decided how many of her sisters would be knocked out at the same time he called Amperes. History has not quite revealed what Ahmed discovered, but we can be sure of the results!
Skip forward a few centuries…
Since we live in a different country, and don’t have too many volunteering wifes/girlfriends available for our tests, we have to invent a different way of testing and explaining the Volts and Amps.
Imagine my surpise, when I discovered that we have such examples right here, in the Mourne Mountains. As I was travelling through said mountains the other day, I was observing the melting snow (in April!) and the little waterfalls that the melting snow created.
Eureka, the perfect example! The amount of water flowing down is equivalent to the Amps, and the speed of the flow is determined by the height difference between the location of the melting snow and the final destination. So if you have loads of water (Amps), and a very small height difference (Volts) you can see there will be a relatively low current. (No need to translate that). Then take the same amount of snow, and put it on top of the hill and the water rushes down, because the Voltage is now much higher. On the way down the water encounters Resistance (Ohms) in various forms. See, it’s all easy!
The moral of this story is that there is a relation between Volts and Amperes and Ohms.
Ohms = Volts divided by Amps.
Amps times Ohms = Volts and
Volts divided by Ohms = Amps.
If you think about it for a bit, it will make sense! Just replace the Amps with amount of water, the Volts is the height the water is falling, and the Ohms the obstacles the water encounters on it’s way. You will never be confused about the Volts and Amps again!
However, we are still none the wiser about How Much any of these things is. Big, bigger, loads, tiny bit??
Luckily, beeing a pint loving nation, we soon have that sussed. We all are aware of the extreme importance of getting a pint that is the same, no matter which pub serves you this heavenly brew. To make sure we all had the same pint we invented the pint glass. (No use having the pint without the glass, right?) So now we had a pint glass and went about making sure the landlords served the right amount of fluid to each of us punters. Great. We are happy. One universal pint, no quibbles. Until…
The owner of the glassworks decided that it would be cheaper to have someone else make the pintglasses. He simply asked them ‘send me a load of pintglasses’. And you will already have figured out, that things from farawayplaces are usually different from what you make yourself. Some time after the new pintglasses were sent to the happy customers, trouble started. Landlords were accused of ‘you served me short’. The opposite cry was probably never uttered. But honesty requires we mention te possibility that someone cried ‘you served me long’. (Of course this language was never actually used, however since this is a nice story, I can not quote the actual words used).
This was a nuisance of major proportions. But the clever blokes we are, we soon got around that one by inventing the %, which simply is a shorthand way of saying: my pint is the same as yours. (The two little circles are symbolic pints, I don’t need to explain.)
That was all great, but what if my pint was smaller then his? mmmm…. Some pints later, after mulling over this problem, (in fact, rumour has it, that it was 100 pints later) it was decided that it would be a good idea to say that if two pints contained exactly the same amount of beer, (lets skip the method of measuring ‘exactly’, since that involves even more beer) we would say they were 100% the same!
Hah! now we’re drinking. And a whole new mathemathics was born, jobs were created, life was good. And kids soon figured out it was a lot easier to ask their parents for a 50% pint. All they had to do was ask twice, to get the same amount..
Due to the enormous amount of pintglasses around, it soon became a bit impractical to test each pintglass. And truth be told, most customers could not really tell the difference between a 95% pint and a 105% pint, als long as the lights were low and the craic was great. For the landlords it did not really matter, because on average the pint was a pint, and each cask more or less contained the same amount of pints, and because of spillage they could never be sure how many pints were in the cask to begin with, and they did not really care anyway. After a while they did not really want to pay for expensive 100% pint glasses, when cheapy 95105% glasses would be acceptable to the punters. (And the reader will observe, that it soon became custom to shorten the 95105% notation to 5% in order to save ink.) Next time you have a drink, you can ponder about that question, is this pint a pint?
Can we pleeease go back to Volts and Amps, I hear you cry… Ok, I’m just having a great time, and since the interweb is down anyway, I might as well write a good story..
Lets recap: You just learned about the Volts and Amps and about tolerances right? Yes you do, say yes please. I don’t want to repeat all this!
A Volt is only a Volt if we can measure it with something accurate. A Volt measured with a 10% meter is not the same as a Volt measured with a 0.1% meter. That’s actually not true, the Volt is the same, what you think it is (measure), is something different.
And so we enter into the murky world of: Is What I See Really What It Is?
Or more precise: what I measure is only as accurate as the tolerance of my measuring instrument. And to shatter a digital myth here and now: Just because it’s digital does NOT mean it’s accurate! True, compared to pintglasses, our measuring devices are unbelievable accurate. But, not as accurate as we like to believe!
Typical DVM’s have an accuray of 1% (DIYMaplin range). Many, gadgets we use have an accuray of 3%. That bad huh.. Yup. Because standard components used in electronics have a 5% tolerance in their values. And that’s because we are so good! 10% is what you buy in the shop, but within a batch of components, the spread is probably 5 % or better.
I got 10 pcs 1% resistors the other day, their values as measured by my 1% DVM were:
99.7 99.9 100.2 100.3 100.4 100.4 Ohm. (the others were worse)
All within specs. But are they any good for what I need? (What do I need them for anyway?)
Lets build ourself a Circuit. (This involves soldering wires together, and in general having fun explaining to the hotel manager that you are only trying to test a theory. All I can say is that hotel managers in NI do not seem to understand, and as a result I was banned from accessing the interweb.)
My circuit was nothing more then 6 resistors glued end to end. Or to put it more precisely, wired in series.
Now if I were to connect the ends of this string to a Voltage producing Gadget (A bunch of Ahmed’s battereeeeh’s or if available, a 5 cell Lipo) a certain current will flow through these resistors. The higher the value of the resistors, the lower the current and vice versa.
Since I had the equivalent of 20.6 Volts handy and the bloke at Maplins only had 10 pcs of 100 Ohm resistors, we can calculate some important things.
R1 
99. 7 
Ohm 
R2 
99.9


R3 
100.2


R4 
100.3


R5 
100.4


R6 
100.4


Total R 
601.1

Ohm 
6 resistors of 1% 100 Ohm, wired in series creates the same value as 1 resistor of 600 Ohm. I can calculate the current running through this string by dividing the Voltage by the resistance (Ohms). 20.6 (Volts) devided by 600 (Ohms) = 0.0342 (A). So the total current through the string of resistors is 0.034 Amps. (A common way of writing this would be 34 milliAmps. )
Ah, but this is only true is the total of all resistors was indeed 600 Ohm. Yup, and it was not! Remember, the total added up to 601.1 Ohm. You are so 100% absolutely right, but let’s keep the maths simple, just pretend for a minute it was 600, ok?)
We do remember that Voltage is Current times Resistance. V=A*Ohm. (Most tesxtbooks will show this as U=I*R, since that is the official way of expressing a Voltage, current and resistance)
We know that the current throught the string was exactly 34.2 mA. not 34.01, or 33.99, but 34.2, because our 1% accurate meter says so.
O dear, the meters accuray is 1% so it could very well be 34.543 or 33.858 and still be ‘accurate’. (And my meters scale was 0 to 20 Volts, it would be 1% of the full range. Usually the scale is not 100% linear either)
But let’s not worry for the moment. I have the only 100% accurate DVM in the universe. Honestly. And we are not really interested in absolute values, we want to know the relation of the values to each other!
So, lets say, I have exactly 34.2 mA through my resistors.
And I have exactly (as measured with my 100% accurate DVM) 20.6 Volts connected to the end of the string of resistors.
Lets do something funny. Let’s measure the voltage accross each resistor. Each resistor has a slightly different value ( my meter tells me so) Lo and behold, I measure approx 3.4 volts accross each resistor.
3. 437 
Volt 
3. 443 
Volt 
3. 454 
Volt 
3. 455 
Volt 
3. 458 
Volt 
3. 46 
Volt 
Wow!! so which on is accurate? The second one? Because we thinks it is 100 Ohm?
Remember, this was a test circuit with resistors that have a value that is within 0.2/+0.4% of 100. (or so we think)
And the casual observer will cry: But you started out with 20.6 Volts!! True, my meter says so, but to measure something in the lower voltage range I switch to a different range on the meter, and now I have no idea what I measure 😉 Yes, my Friends, that’s Life in Electronics. It all works on grey smoke, and no one has a clue how it manages to work at all! And I am not joking. Electronics is all about trying to make the tolerances of parts work in your favor and at best stop them behaving badly.
Using an 18 Volt supply (giving me a 30 mAmp current) to make the maths easier I can see that:
R1 
95

Ohm 
2.8595

Volts 
R2 
105

Ohm 
3.1605

Volts 
Above is what you measure if you use standard 5% resistors. Shocking, right? Yes, indeed.
Below are the values you can expect using standard unselected 1% resistors.
R1 
99

Ohm 
2.9799

Volts 
R2 
101

Ohm 
3.0401

Volts 
It gets worse. In the above example I use a 100% accurate Voltmeter.
What happens if I use a meter that has an 1% accuray (as in: value could be +/1%)
R1 
99

Ohm 
2.9799

Volts 
1

2.950134

3.0097324

R2 
101

Ohm 
3.0401

Volts 
1

3.009732

3.0705351

So, worst case: my 3.000 volts could actually be somewhere between 2.95V and 3.07V and still be within 1% specs.
3% components give me anywhere between 2.83 and 3.19Volts. And so far I have only used a single voltmeter.
If you use a circuit that has to scale voltages to be able to be measured,.it really gets exciting.
Scaling is often/always needed, because most voltmeters only have a certain range they can measure. In our world of digital wizardry, a common range would be 05 Volts. To measure higher voltages, one would introduce a voltage devider, (as the names suggests, it divides one higher voltage to a lower one, that fits into the range of our measuring device. ) Of course all these components have a tolerance)
I’m sure by now you see that we actually have no hope at all of measuring anything at all with any amount of accuray.
But to return to the beginning of the story, the Missing Volts.
This whole ramble was caused by one of our esteemed clubmembers mentioning the fact that one cell in his LIPO’s always indicates a higher value on his measuring thingy.
Since it happens on all packs, my suspicion is the measuring gadget. And without feeding it with some accurate voltages to test it, we do not know what it measures!
To be continued, errors fixed, and story completed with more results!
Kees
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